In this study, a relativistic formulation of the $(q)$-deformed Dunkl-Fokker-Planck equation in $(1+1)$-dimensions is constructed within the reflection-deformed quantum framework. In this case, the formalism includes $(q)$-deformed Dunkl operators and reflection symmetry to build a generalized dynamical structure for a relativistic quantum systems framework. Moreover, the corresponding $(q)$-Wigner-Dunkl supersymmetric configuration is established via the construction of deformed ladder operators and supersymmetric algebraic relations, yielding a consistent spectral representation of the model within the algebraic framework. The analysis extends to the harmonic oscillator with centrifugal interaction, where exact algebraic solutions, similarity reduction techniques, and closed energy spectra are obtained analytically in detail. The role of the deformation parameter and reflection operator on spectral properties and wavefunction structure is examined systematically in detail. A generalized Foldy-Wouthuysen (FW) transformation is introduced within the deformed Dunkl framework to achieve relativistic decoupling of positive- and negative-energy sectors within the present theoretical formulation. In this case, this approach yields an effective reduced Hamiltonian, including higher-order relativistic and deformation-induced terms. Also, the associated Dunkl-Fokker-Planck dynamics generated through high-order FW reduction are examined in detail for reflection-deformed relativistic quantum systems. In this context, results obtained here yield a unified algebraic and relativistic description of $(q)$-deformed Dunkl structures and construct a consistent framework for investigating supersymmetric and relativistic properties in reflection-symmetric quantum models in general.

We study local quantum field theories in Anti-de Sitter (AdS) space, with boundary conditions that break some of the bulk isometries. Specifically, we focus on conformal defects and we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present. The existence of a displacement was conjectured in arXiv:2508.08250 for Wilson loops in Yang-Mills theories in AdS. Our proof is valid in general and applies, in particular, to defects in long-range models, as we discuss in various examples. In the bulk, the modes sourced by the protected operators have Compton wavelength of order of the AdS radius: they constitute the AdS analogue of the Goldstone bosons for the spontaneous breaking of the corresponding symmetries.

We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form $\mathbb{Z}_k$ for each primitive Pythagorean triple $a^2 + b^2 = k^2$. The theory is self-dual under gauging any of these symmetries, and so to each there is associated a non-invertible topological defect. We study the properties of these lines, and show that any conformal boundary condition of two Dirac fermions that preserves a $U(1)^2$ symmetry can be found by dressing a trivial Dirichlet boundary with one of them. We discuss two microscopic descriptions of these defects: fermions coupled to a quantum-mechanical rotor degree of freedom; and an abelian gauge theory that realises symmetric mass generation in a half-space.

We construct families of deformations of the double-scaled SYK (DSSYK) model and investigate their bulk interpretation. We introduce microscopic deformations of the SYK model which, after ensemble averaging and in the double-scaling limit, are described by a transfer matrix encoding the recurrence relations of basic orthogonal polynomials in the q-Askey scheme. For certain families of deformations in the semiclassical limit at finite temperature, the chord number (encoding Krylov complexity) corresponds to the length of an Einstein-Rosen bridge connecting an End-Of-The-World brane to an anti-de Sitter asymptotic boundary. By increasing one of the deformation parameters, the models eventually exhibit discrete energy levels, signaling a new geometric transition in sine dilaton gravity. Via the SYK-Schur duality, Krylov complexity also admits a representation-theoretic interpretation as the spread of the SU(2) spin in the index of an $\mathcal{N}=2$ SU(2) gauge theory. We study the operator algebras of the deformed theories. The algebras can be type II$_1$ or type I$_\infty$ factors, depending on the operators that are included. The entanglement entropy between the type II$_1$ algebras for a pure state manifests as an extremal surface through the Ryu-Takayanagi formula. We discuss connections between our results and the emergence of baby universes in the bulk.

In the presence of extended defects, familiar incoming particles can scatter into exotic outgoing states created by twist operators. We show that one possible mechanism driving these "categorical scattering" processes is the presence of localized 't Hooft anomalies on the defect's worldvolume. Defect anomalies trap non-trivial charges at junctions between the symmetry lines and the interface, opening new transmission channels that would naively appear to violate selection rules. After outlining the general mechanism, we investigate several concrete examples with defects, interfaces, and boundaries. For models of massless chiral fermions already studied in the literature, we show that the emergence of twist operators can be understood as a consequence of defect anomalies. We then introduce new massive integrable theories in which a similar phenomenon occurs, and we explicitly solve the associated scattering problem, obtaining new integrable solutions. Finally, we construct lattice spin chains with defects where similar physics is expected to arise.

We revisit the Hartle-Hawking wave function in AdS spacetime, where natural spatial slices are open and require an additional spacetime boundary. This leads to two constructions: a fully gravitational wave function, in which the boundary configuration is integrated over, and a partially frozen one, in which it is fixed, as in AdS/CFT. To illustrate the fully gravitational construction, we explicitly analyze it in AdS$_3$ Einstein gravity and AdS$_2$ Jackiw-Teitelboim gravity. We then evaluate the one-loop correction to the hyperbolic-ball partition function in $D$-dimensional AdS Einstein gravity, expected to give the leading contribution to the wave-function norm. We demonstrate that the fully gravitational hyperbolic ball partition function, where the boundary fluctuates, develops a nontrivial one-loop phase of $(\mp i)^{D+1}$, analogous to that of the sphere partition function in dS gravity. By contrast, the partially frozen partition function, where the boundary is fixed, remains real and positive. Motivated by this AdS comparison, we conversely investigate a partially frozen dS sphere partition function where the metric on an equator is fixed, finding that its one-loop phase cancels nontrivially. Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.

We study quantum mechanics of bosonic multi-matrix Lagragians in the collective field framework, with particular emphasis on three matrix models. We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability.

For a local quantum field theory in anti-de Sitter space with conformal boundary conditions but without dynamical gravity, the boundary theory is generically a non-local conformal field theory. Such theories can support conformal defects, but the standard local-CFT arguments based on a boundary stress tensor and conserved currents do not apply. We argue that, under general assumptions, displacement and tilt operators nevertheless exist and have protected quantum numbers. The mechanism is a Goldstone-type phenomenon in AdS: defect-induced symmetry breaking on the boundary is spontaneous from the viewpoint of the local bulk theory, whose Ward identities enforce the corresponding protected defect operators. We illustrate the mechanism in weakly coupled defect RG flows, long-range Landau--Ginzburg models, 4D Maxwell theory, and Yang--Mills theory in AdS.

We present a comprehensive analysis of the Landau-Khalatnikov-Fradkin transformations for the charged fermion propagator in reduced quantum electrodynamics (RQED). Starting from the propagator in a reference gauge, we perform a gauge transformation to obtain its analytical expression valid to all orders in an arbitrary covariant gauge and also applicable in a nonperturbative context. This work complements and extends previous studies of quantum electrodynamics in various spacetime dimensions, for both massless and massive fermions. At the perturbative level, we expand the resulting expressions up to two-loop order for both massless and massive cases, and compare our results with those available in the literature wherever possible. We argue that the most suitable choice of the reference covariant gauge in RQED is $\xi=1/3$, as in this case the leading logarithmic contribution to the massless wave-function renormalization vanishes at one-loop order. This choice provides a direct connection between perturbation theory and the constraints imposed by multiplicative renormalizability on the massless fermion propagator. We also investigate the implications of the Landau-Khalatnikov-Fradkin transformations for the dynamically generated mass function of the fermion propagator. Finally, through numerical computation, we demonstrate that both the chiral fermion condensate and the fermion pole mass are gauge-invariant quantities.

This work concerns scalar field theories with topologically nontrivial vacuum manifold in rotationally symmetric backgrounds of arbitrary dimension. Lagrangians with canonical and generalized kinetic terms are considered, and a Bogomol'nyi framework is developed for the symmetric restriction of the theory. Localized topological solutions are found. Their stability, which would normally be prevented in higher dimensions due to scaling instability, is made possible by the presence of an explicit radial dependence on the potential. The first-order equations give rise to an integrable orbit equation which can be used to solve the problem completely. It is shown that target space orbits - but not the solutions themselves - are shared between analogous systems defined in different backgrounds. Moreover, the first-order equations can be mapped into a one-dimensional BPS theory through a transformation encoded by a function $\xi(r)$. The internal structure, size and existence of defects follows from the properties and range of this mapping. We use these tools to evaluate the effect of geometry on confinement, existence, and structure of solitons. Exact solutions are provided in Minkowski, Schwarzschild, de Sitter, Schwarzschild de Sitter and conformally flat backgrounds.

In Plebański nonlinear electrodynamics with spontaneous Lorentz symmetry breaking, nontrivial magnetic backgrounds are selected by stationary points of an effective Hamiltonian. Previous branchwise Hamiltonian analyses showed that this same stationarity requirement coincides with the vanishing of the determinant of the Poisson-bracket matrix among the second-class constraints, but the structural origin of this coincidence was not manifest. We show that it follows from the constitutive origin of the theory. The structural potential \(V(P,Q)\) generates the electromagnetic constitutive relations, while the effective Hamiltonian for magnetic vacua is the complementary energy associated with the magnetic response at fixed \(\Dvec\). Moreover, because the first-order constitutive relation enters the Dirac constraint structure, the magnetic constitutive Jacobian appears as a local block of the Poisson-bracket matrix among the second-class constraints. This complementary-energy structure implies that every nontrivial magnetic stationary point lies on a surface where the linearized map \(\delta\Hvec\mapsto\delta\Bvec\), at fixed \(\Dvec\), loses rank. We use this interpretation to formulate the reduced linearized theory at the vacuum, discuss the removal of the radial mode in the vacuum-restricted theory, and clarify why electric and mixed stationary branches are obstructed in single-invariant models.

We develop bootstrap methods for mixed heavy-light four-point correlators $\langle GGOO\rangle$ in $\mathcal N=4$ super-Yang--Mills theory at large $N$, where $O\equiv {\cal O}_2$ is the chiral primary operator in the stress-tensor multiplet and $G$ are (dual) giant graviton operators with dimension of order $N$, including the maximal determinant case. The loop integrand is expanded in a basis of labelled $f$-graphs -- necessarily including non-planar topologies due to the dimension-$N$ nature of the giant gravitons -- and the coefficients are fixed by various bootstrap conditions including double-triangle and triangle rules in the cusp and OPE limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry, the latter also allowing extension to correlators involving generic chiral primaries $\mathcal{O}_k$. Together, these inputs uniquely determine the correlator through three loops, passing further non-trivial consistency checks. For the maximal determinant operator, we reproduce the known results through two loops and obtain the full three-loop correction.

Black-hole formation is expected, via holography, to correspond to thermalization in the boundary theory. For open quantum systems, an initial pure state generically evolves into a mixed state irreversibly, suggesting that horizon formation in the bulk should arise. In this paper, we extend the holographic Lindblad prescription to a non-Markovian setting and apply it to JT gravity coupled to a scalar field. Using numerical simulations in the semiclassical and high-temperature regime, we demonstrate the dynamical formation of black holes.

We study the linearized scattering of dilaton-graviton waves from a thin brane in three-dimensional spacetime. Holographically, the setup models scattering from an interface in a family of strongly coupled theories related to dimensional reductions of higher-dimensional $AdS_{d+2}$ gravity. Unlike the pure $AdS_3$ case, for $d>1$ the physical bulk mode allows incident radiation to be redistributed into reflected, transmitted, and evanescent components. For the $d=2$ background, we obtain a controlled solution in which the interface acts like a rough translucent window, producing diffuse angular scattering and absorption into surface modes. From the dual perspective, the scattering process is suggestive of dissipative flow toward the infrared. For $d=4$, the same analysis reveals a sensitivity to the infrared boundary condition, suggesting that the singular zero-temperature geometry must be regulated in order to have a well-defined scattering process. The structure of the equations nevertheless suggests that a regulated $d=4$ problem may exhibit the same qualitative redistribution of incident flux.

We study the $\alpha'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruipérez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective action on $\mathbb{T}^{6}$ followed by a truncation and a field redefinition. We show that the metric of spaces of self-dual curvature does not receive any corrections, but their (initially trivial) dilaton and axion fields do, owing to their couplings to Gauss--Bonnet and Pontrjagin densities. We find the generic form of the corrections of the dilaton and axion fields for the Gibbons--Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub--NUT and Eguchi--Hanson spaces. We construct the boundary terms required to define a well-posed Dirichlet variational principle in the Euclidean Cano--Ruipérez theory, including the contributions associated with the Gauss--Bonnet and Pontrjagin terms. The boundary terms are normalized for asymptotically-locally-Euclidean solutions, and we evaluate with them the Euclidean action of the $\alpha'$-corrected Eguchi--Hanson instanton showing that the total action receives no corrections to first order in $\alpha'$. We also show that, at zeroth order in $\alpha'$, one can construct Euclidean solutions similar to the string theory D-instanton with non-trivial dilaton and axion on the background of a self-dual purely gravitational instanton which remains unmodified. We also compute the $\alpha'$ corrections to these solutions.

A consistent non-compact axion cosmology requires a non-periodic field, an effective field theory valid sufficiently above the inflationary scale, and a small non-QCD contribution to the potential that tilts the axionic vacuum landscape in order to trigger a timely domain-wall collapse. All conditions can be met by the dilaton -- the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance.

A three-dimensional $\mathcal{N}=4$ gauge theory is constructed whose Higgs branch realizes the affine closure of the cotangent bundle of the minimal nilpotent orbit of $\mathfrak{sl}_n$. This space is a symplectic singularity recently identified by Fu and Liu as a $\mathrm{U}(1)$ hyperkähler quotient of the closure of the minimal nilpotent orbit of $\mathfrak{so}_{2n+2}$. The theory arises by gauging an $\mathrm{SO}(2)\cong\mathrm{U}(1)$ subgroup of the flavour symmetry of $\mathrm{SU}(2)$ SQCD with $n+1$ flavours. The Hilbert series is computed and the stratification is determined. A non-simply laced magnetic quiver is proposed whose Coulomb branch reproduces the same singularity. Evidence is thereby provided for a mirror pair involving a non-simply laced quiver, further tested through quiver subtraction and Hasse diagram inversion. A related $\mathbb{Z}_2$ quotient of the magnetic lattice is also analysed, and the exceptional behaviour in the case $n=2$, where $A_1 \cong C_1$, is explained. This construction provides a concrete example in which the Higgs-branch structure associated with a non-simply laced magnetic quiver can be inferred and validated through its mirror dual.

In the Kerr-Schild double copy, static and spherically symmetric black hole solutions of general relativity are mapped to purely electric solutions of Maxwell's theory in flat spacetime. We demonstrate that, for these configurations, the thermodynamic Smarr formula is structurally identical to the single-copy Gauss's law. Extending this to asymptotically anti-de Sitter spacetimes, we prove that the thermodynamic pressure-volume term ($PV$) naturally emerges from a gauge-theoretic background subtraction. This relationship establishes a novel connection between the classical double copy and black hole thermodynamics.

We provide a comprehensive overview of the current status of higher-codimension defect systems. We review the holographic description and field theoretic properties of codimension-2 defects within the framework of defect Conformal Field Theories (dCFTs). Starting from the well-established classification of $1/2$-BPS supersymmetric defects, we examine their realisation through probe branes and bubbling supergravity geometries. Special emphasis is placed on recent developments involving non-supersymmetric D3/D5 configurations and their holographic interpolations. We discuss the calculation of important physical observables, such as one-point functions of the stress-energy tensor and chiral primary operators, across both weak and strong coupling regimes. The agreement of the results in the two regimes exhibits the full power of the holographic principle. This is a proceedings contribution to the Athens Workshop in Theoretical Physics: 10th Anniversary, held at the National and Kapodistrian University of Athens on December 17-19 2025.

The AMPS firewall argument relies on treating early radiation, late outgoing Hawking modes, and interior partner modes as approximately independent quantum subsystems. In diffeomorphism-invariant quantum gravity, however, gravitational dressing and asymptotic constraints obstruct such a tensor-product factorization of physical observables. In this essay, we sharpen this obstruction by formulating subsystem independence directly in operator-algebraic terms. Using modular theory, half-sided modular inclusions along null directions, and the sector-wise maximality of the dressed radiation algebra at future null infinity, we show that -- within a fixed asymptotic charge sector -- the algebra associated with the interior Hawking partner cannot form an independent commuting subalgebra, but must be contained as a (non-commuting) subalgebra of the radiation algebra itself. The subsystem-independence assumption underlying the AMPS paradox therefore fails, and the entanglement-monogamy step never becomes applicable. As a result, unitary black hole evaporation and semiclassical horizon smoothness are compatible in asymptotically flat quantum gravity, without invoking entanglement islands, replica wormholes, or modifications of semiclassical horizon physics.

In this paper, we investigate how AdS scalar propagators are represented in the celestial basis. Starting from the standard bulk-to-boundary propagator in Euclidean AdS space, we express the propagator in a Schwinger parametrization and construct the corresponding boundary-to-boundary propagator. We then transform the resulting propagators to the celestial basis using conformal primary wavefunctions for both massless and massive scalar fields. For the massless case, the celestial propagator reduces to an effectively two-dimensional boundary-to-boundary object on the celestial sphere dependent on the AdS/CFT conformal dimension $\Delta$. For the massive case, the celestial propagator exhibits a nontrivial kernel involving modified Bessel functions, closely resembling the momentum-space radial structure of AdS bulk-to-boundary propagators. The results suggest a structural translation from AdS propagators and celestial propagators.

The gravitational path integral produces an asymptotic expansion in $G_N$, a fact which is puzzling in the case of observables that are expected to fluctuate wildly. Wormholes appear to compute ensemble averages of functions of such observables, though in typical constructions of AdS/CFT, there are no parameters to average over except, in some examples, a single integer $N$. We introduce a procedure that we call ``Mellin averaging'' to define a sort of asymptotic average of a function of $N$. We argue that Mellin averaging over $N$ may suffice to reproduce the apparent randomness seen in wormhole physics, provided that the dual theory admits an analytic continuation in $N$ and the relevant observables fluctuate on superpolynomially small scales in $N$. As a test case, we consider the spectral form factor in the regime where the double cone is believed to dominate the gravitational path integral and compare to a random matrix theory in which $N$ behaves as a continuous variable. We also describe some toy models of analytic continuation in $N$: a qubit model that can be analytically continued in $N$, and an explicit construction of a deterministic function of $N$ that simulates a sequence of independent draws from a Gaussian ensemble.

It has been known for a long time that initializing weight matrices to be orthogonal instead of having i.i.d. Gaussian components can improve training performance. This phenomenon can be analyzed using finite-width corrections, where the infinite-width statistics are supplemented by a power series in $1/\mathrm{width}$. In particular, recent empirical results by Day et al. show that the tensors appearing in this treatment stabilize for large depth, as opposed to the tensors of i.i.d.-initialized networks. In this article, we derive explicit layer-wise recursion relations for the tensors appearing in the finite-width expansion of the network statistics in the case of orthogonal initializations. We also provide an extension of recently-introduced Feynman diagrams for the corresponding recursions in the i.i.d.-case which are valid to all orders in $1/\mathrm{width}$. Finally, we show explicitly that the recursions we derive reproduce the stability of the finite-width tensors which was observed for activation functions with vanishing fixed point. This work therefore provides a theoretical explanation for the stability of nonlinear networks of finite width initialized with orthogonal weights, closing a long-standing gap in the literature. We validate our theoretical results experimentally by showing that numerical solutions of our recursion relations and their analytical large-depth expansions agree excellently with Monte-Carlo estimates from network ensembles.

The gravitational field of two-body system, a high energetic particle and a massive particle at rest, is studied in the linearized Einstein gravity. The ultrarelativistic particle yields a plane-fronted gravitational shockwave which perturbes gravitational field of the particle at rest. The problem can be also considered as a fixed-target high energy collision. We show that this collision is accompanied by the gravitational radiation, as is expected from the earlier results on the high-energy scattering. The new effect is a secondary spherical gravitational shockwave when the initial shockwave hits the massive particle. In the considered approximation the flux of gravitational radiation and the amplitude of the spherical shockwave are found in an analytic form. The suggested approach is also applicable when the null particle is replaced by plane null shells of a general profile. Implications of these effects for astrophysics are shortly discussed.

External matter distributions can substantially reshape the strong field environment of compact objects, yet this effect is usually neglected in idealized isolated models. In this work, we investigate geometrically thin, optically thick relativistic accretion onto a static axisymmetric space-time that describes a slightly deformed compact object immersed in an external quadrupolar field as an exact solution of vacuum Einstein field equations. Our aim is to determine whether such locally geometries can produce distinctive accretion signatures and, more broadly, to identify the physically meaningful radial domain over which the local solution remains self-consistent. We show that the external quadrupolar distortion leaves a clear imprint on both orbital dynamics and accretion structure. We further find that the outer edge of the radiating region is closely tied to the transition between radiation pressure and gas pressure dominance, which may link the geometry to the thermodynamic properties of the flow. Therefore, the local nature of the distorted spacetime is not merely a formal geometric feature, but has observable consequences for the morphology and emission properties of accretion flows.

In this work, we derive an exact black hole solution in higher-order curvature gravity by coupling an electromagnetic sector formulated within the ModMax framework to a quintessence dark energy component. Focusing on purely electrically charged configurations, we analyze the thermodynamic and geothermodynamic properties of the solution to investigate its stability and phase structure. Within this sector, the ModMax theory effectively reduces Maxwell electrodynamics up to a rescaling of the electric charge, and thus the obtained solution corresponds to a consistent subset of the broader nonlinear theory. Using thermodynamic geometry, we examine microscopic interactions and phase transitions, showing that divergences in the thermodynamic curvature coincide with the vanishing of the heat capacity, confirming the consistency of the phase structure. We further explore the optical properties of the black hole by studying null geodesics and determining the photon sphere and the corresponding shadow radius for different values of the quintessence state parameter $\omega$. Exact analytical expressions for the photon-sphere radius are derived, revealing that higher-order curvature corrections and quintessence significantly enhance the shadow size, whereas the electric charge has the opposite effect. Notably, quintessence is found to have a more pronounced impact on the shadow than the charge. These results highlight that dark energy and higher-order curvature corrections can yield potentially observable signatures in black hole shadows.

We prove that any background-inert perturbative coupling $ \lambda $ in coincident $ f(Q) $ gravity exhibits a degeneracy with the clustering amplitude $ \sigma_{80} $, when using compressed CMB distance priors. This degeneracy is, in fact, a direct materialization of a more deeper $ A_s-D_0(\lambda) $ degeneracy between the primordial amplitude $ A_s $ and the present day growth factor $ D_0(\lambda) $. We outline a consistency check scheme, applicable to models even outside the $ f(Q) $ class, by computing $ A_s $ needed to reproduce the $ \sigma_{80} $ predicted by the sampler. We perform our analysis with two dataset pipelines, based on the coupled/decoupled $ f\sigma_8(z) $ data. To ensure theoretical diversity, we include $ \Lambda $CDM and the Hybrid model in the $ f(Q) $ framework. Our results illustrate that adding the $ \lambda_0\sqrt{QQ_0} $ correction to the models inflates $ \sigma_{80} $ to unphysical values, while showing moderate evidence in favor of the said models. However, this results in an increase of $ 20\%-30\% $ in $ A_s $ in $ 1.7\sigma-2.2\sigma $ tension with Planck values. We utilize the $ 1\sigma $ $ \ln(A_s) $ constraints from Planck as priors in order to fix the artificial increase in $ \sigma_{80} $ and find that all the constrained parameters return to their baseline values. Each model is penalized by around $ 2 $ units per extra parameter. Interestingly, the $ \Lambda $CDM$ +\lambda_0+\ln(A_s) $ + SDSS DR16 combination shows a weak preference over the vanilla $ \Lambda $CDM model, validated by the values of $ \log\mathcal{Z},\;AIC,\;DIC, $ and BIC.

A comprehensive study of the phase structure of the two-flavor quark-meson-diquark model is presented within the nonperturbative functional renormalization group framework. The influence of mesonic fluctuations beyond the mean-field approximation is investigated, and two-point functions of the diquark fields are computed at finite real-time frequencies. Renormalization group consistency of the effective potential is ensured in order to avoid cutoff artifacts. Substantial modifications of the phase structure are found once mesonic fluctuations are included, and for sufficiently strong diquark couplings the dynamics become dominated by diquark condensation. These effects are elucidated through an analysis of the diquark pole mass and the Silver-Blaze property.

For three-dimensional non-interacting multi-band metals, we show that important information about the shape and the quantum geometry of Fermi surfaces is encoded in the subleading logarithmic term of bipartite charge fluctuations. This logarithmic term is related to the dimensionless $|\mathbf{q}|^3$-coefficient of the structure factor in momentum space, and both quantities can be expressed as Fermi surface integrals of the Fermi surface curvature tensor and the quantum metric tensor. When the real-space partition surface is a quadric (i.e., sphere or ellipsoid), the logarithmic coefficient satisfies a topological bound depending only on the Euler characteristic and the Chern number of the Fermi surface, illustrating a non-trivial interplay between topology and quantum topology in multi-band metals.

We construct a new Ricci-flat metric by demagnetizing the recently reported Kerr-Bertotti-Robinson (KBR) solution. The metric is a deformation of the Kerr metric characterized by a parameter $B$, so that the asymptotic Kerr becomes a regular dome of spindle shape with north and south poles. Despite lacking an asymptotically-flat region, we find that the first law of black hole thermodynamics can be established. Some thermodynamic relations are identical to those of the Kerr black hole, as if the constant $B$ is absent. Our Ricci-flat rotating metric serves a neutral seed for a variety of inequivalent schemes of magnetizing the Schwarzschild and Kerr black holes.

We construct charged black hole solutions in bumblebee gravity coupled to a general class of nonlinear electrodynamics (NLED) using an auxiliary Maxwell-scalar formalism. The norm-fixed radial configuration of the bumblebee vector makes the solutions asymptotic to a conical Lorentz-violating vacuum and requires stringent nonminimal bumblebee-NLED couplings. The general black hole solutions contain independent mass and charge parameters. There are two sources of singular behavior at the center: one is due to the Schwarzschild-type pole and the other is the residual conical singularity of the Lorentz-violating vacuum. By fine-tuning the mass-charge relation, one can generally remove the pole singularity, giving rise to marginally regular black holes. For a suitable NLED theory such as Born-Infeld theory, both singularity sources can be removed at the cost of requiring both the mass and the charge to be fine-tuned to specific functions of the coupling constants. The resulting solutions describe regular horizonless spacetimes interpolating from AdS or dS cores to Lorentz-violating vacua.

We construct new families of everywhere regular, asymptotically flat solitons in the Einstein--Proca model, obtained as self-gravitating continuations of flat-spacetime (singular) Proca multipoles. First we consider static and axially symmetric solutions, organized by a multipole number $\ell$. Two distinct classes arise: electric-type configurations, which include the spherical Proca stars as the $\ell=0$ case, and magnetic-type configurations, which have no spherical counterpart and start at $\ell=1$. Then we construct hybrid solutions as nonlinear superpositions of electric and magnetic multipoles. These have non-vanishing local angular momentum density but vanishing total angular momentum, and in some cases have no north-south $\mathbb{Z}_2$-symmetry. By performing dynamical evolutions of Proca stars in the new magnetic and hybrid sectors, we show they are unstable, decaying to the (static) prolate Proca stars or the (stationary) spinning Proca stars, previously identified as dynamically robust, electric sector configurations. In some cases, they can also collapse into a black hole.

Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect.

Graviton lasers have been considered in the past, \cite{gl}, but practical terrestrial implementations appear infeasible. The absence of any known mechanism to reflect gravitons means that it remains unclear how a graviton beam could be directed repeatedly through a putative lasing medium. Astrophysical graviton lasing is still a possibilty as circular graviton orbits around blackholes afford the possibility of an arbitrarily long path length through the lasing medium of ultra-light dark matter \cite{bhgl,nhaxs}. In this essay, we consider the possibility of a graviton laser that could be constructed in a laboratory setting. The graviton lasing medium could be one of many possible gravitating systems, of which we give three possible examples. We calculate the possibility of reflecting the gravitons by using the conversion of gravitons into photons in an external magnetic field, the Gertsenshtein effect, \cite{Gertsenshtein1962}. We may convert the gravitons to photons, then reflect the photons, then reconvert the photons into gravitons via the same effect, and then pass them through the graviton lasing medium. With an identical apparatus on the other side, we can essentially extend the path length of the gravitons through the lasing medium as arbitrarily long as desired.

In this paper, we presented an approximate analytical treatment of the Coulomb plus logarithmic potential using perturbation theory to investigate the mass spectra of bottomonium and charmonium mesons for the low-order quantum states. The derived energy equation, to first-order corrections, was employed to model the free potential parameters through fitting to experimental data of the Particle Data Group. The proposed potential successfully reproduces asymptotic freedom at short distances through one-gluon exchange interactions and quark confinement at large distances, which are the essential features of the strong interactions in Quantum chromodynamics theory. The calculated bottomonium masses exhibited excellent agreement with experimental values, yielding an absolute percentage average deviation (APAD) of 0.24%, which improves upon several previously reported theoretical results. Similarly, the vector and pseudoscalar charmonium masses were obtained with an APAD of 1.65%, demonstrating improved and comparable accuracy relative to existing competing theoretical calculations. Although our results were limited to first-order corrections to the energy spectra within the perturbation theory, the reliability of the approximation was validated by comparison with exact numerical solutions obtained using the matrix Numerov method. The small percentage errors obtained confirm the effectiveness of the phenomenological potential and perturbation approximation in describing quarkonia systems. The results suggest that the approach can be reliably extended to higher excited states.

We present a complete calculation of the one-loop self-energies for all fields in the linear sigma model coupled to quarks at finite temperature and in the presence of a uniform magnetic field. The analysis consistently incorporates thermal and magnetic effects for both neutral and charged degrees of freedom, providing a unified framework valid for arbitrary values of the temperature and the field strength. The computation is performed using the Matsubara formalism to account for finite temperature effects and the Schwinger proper-time representation for charged propagators in a magnetic background. Special attention is given to loop contributions involving particles with different electric charges, for which the associated Schwinger phases do not cancel. We show that these terms can be systematically evaluated in coordinate space using the Ritus formalism, which provides the appropriate framework for treating external charged states in the presence of a magnetic background, and consistently expressed in momentum space. The resulting expressions exhibit a nontrivial interplay between thermal fluctuations and magnetic effects and allow for a clear separation between vacuum and matter contributions, providing a well-defined structure for the identification of ultraviolet divergences. Our results establish a consistent and systematic framework for the computation of thermomagnetic one-loop corrections in effective models of QCD, capturing the full interplay between thermal and magnetic effects for all dynamical degrees of freedom.

We study the impact of symmetry energy ($S$), hyperons, and dark matter (DM) on structural and oscillatory properties of neutron stars (NSs). Uncertainty from hadronic equation of state for NSs is considered with 15 relativistic mean field models having slope parameter ($L_0$) of $S$ in range $40-120$ MeV. DM admixed NSs (DMANSs) are described with feeble interaction between light DM fermions ($\chi$) with hadronic matter in the presence of hyperons via scalar ($\eta$) and vector ($\xi$) dark mediators. The masses $m_{\chi}$, $m_{\eta}$ and $m_{\xi}$ are related by self-interaction constraints from bullet cluster. DM self-interaction couplings are related to $m_{\chi}$ by relic density constraint. The DM density is taken as an exponential function of baryon density with a free parameter $\alpha$. Uncertainty from DM model is incorporated by exploring the dependence on $m_{\chi}$ and $\alpha$. Several DM search experiments have almost ruled out the existence of massive DM ($\gtrsim$ GeV). Lately, pursuit for sub-GeV DM has attracted significant attention. Therefore, we consider $m_{\chi}<$ 1 GeV and $\alpha \leq$ 0.1 such that the contribution of DM to the total mass of the DMANSs is $<10\%$. Comparing our results with various astrophysical constraints, we find that the HESS J1731-347 and GW170817 data are very important in determining the presence of light DM in NSs in moderate amount, relevant in the range $L_0\lesssim$ 58 MeV. Employing models of DMANSs that satisfy several observational data, we infer with Bayesian analysis, the likely ranges of $m_{\chi}$ and $\alpha$ are almost independent of the underlying hadronic model within 40 MeV $\lesssim$ $L_0$ $<$ 58 MeV. In the absence of DM and with the most probable values of $m_{\chi}$ and $\alpha$ obtained from the Bayesian inference, we calculate the frequencies of non-radial $f$- and $p_1$-modes oscillation of NSs/DMANSs.

We investigate the quasinormal modes of massless scalar and electromagnetic perturbations in charged Euler--Heisenberg black holes surrounded by perfect fluid dark matter. The quasinormal frequencies are calculated using the asymptotic iteration method and the sixth-order WKB approximation, and the relative deviation between the two methods is quantitatively analyzed to verify the reliability of results. The greybody factors for both perturbations are also evaluated within the sixth-order WKB framework. We systematically examine the effects of the black hole charge $Q$, nonlinear electrodynamic parameter $a$, dark matter parameter $\lambda$, and angular quantum number $l$ on the quasinormal frequencies and greybody factors. We find that these parameters significantly modify the structure of the effective potential barriers, and thus affect the oscillation frequencies, damping rates, and wave transmission and reflection properties of the perturbed fields.

We investigate the consistency in the thermodynamics and the approaches at the equation and action levels for the quantum-improved charged black holes with scale-dependent couplings. For the quantum-improved Reissner-Nordström black holes, we find that the thermodynamic consistency allows both the Newton and electromagnetic couplings to have arbitrary dependence on the radial coordinate. We point out a subtlety in the chemical potential with the scale-dependent electromagnetic coupling in the study of thermodynamics. We also examine the compatibility of the Einstein equations at the equation and action levels with the Bianchi identity, identifying the need for an additional quantum energy-momentum tensor. We then find that the consistency between the approaches at the equation and action levels requires that the Newton coupling satisfy certain property. Finally, we extend the analysis to cosmological solutions, suggesting that quantum-induced modifications can drive the isotropization of the early universe.

Using the multi-index approach to regularity structures due to F. Otto et al., we construct a regularity structure and a model for it associated to the stochastic Langevin equation for the 3D Euclidean Yang-Mills functional. For the model we also obtain global stochastic and global pointwise weighted Besov type estimates which hold almost surely. The model is defined as a limit of a sequence of smooth models introduced with the help of a mollified noise. When the mollification is removed the sequence converges in a certain topology defined with the help of the stochastic estimates. To obtain these results we develop the multi-index approach for systems of equations with vector-valued white noises. This project is motivated by the problem for constructing 3D Euclidean Yang-Mills measure and by the earlier results of the author on the related problem of canonical quantization of the Yang-Mills field on the Minkowski space.

We investigate the imprints on the angular power spectra of cosmological perturbations of a pre-inflationary bounce phase, as described by the hybrid and dressed metric approaches to loop quantum cosmology. For this purpose, we derive a new parametrization of the primordial power spectrum at the end of the inflationary regime. Apart from slow-roll coefficients and cosmological parameters that are present in the standard cosmological scenario without quantum modifications, this parametrization additionally depends only on pre-inflationary physics. More specifically, we find a dependence on the number of e-folds during the bounce epoch and on a characteristic suppression scale which, given the e-folds accumulated during cosmic evolution, is determined by the energy density at the bounce. Recall that this density depends on the Immirzi parameter and the area gap known from LQG. This leads to a robust and accurate parametrization of the primordial power spectrum. Since in pre-inflationary scenarios there is no preferred vacuum state, we adopt the NO-AHD proposal, which selects a vacuum that is optimally adapted to the background dynamics and yields a non-oscillatory primordial power spectrum. With this choice, we show that the tensor-to-scalar ratio in both quantization approaches coincides with its expression in the standard $\Lambda$CDM model when the observed scales are not much smaller than the power-suppressed region. Computing also the angular power spectrum, we find that, for a total cosmic expansion of about 140 e-folds, both the hybrid and the dressed metric approaches exhibit excellent agreement with Planck data at high multipoles, while apparently improving the fit with respect to $\Lambda$CDM for low multipole numbers.

We show that flying focus fields can be obtained from complex conformal transformation of plane waves, and that solutions of the massless wave equation in the so-obtained fields are, correspondingly, conformal transformations of the Volkov solutions. This leads to the result that photon emission amplitudes in a totally depleting flying focus beam may be computed directly from the corresponding plane wave amplitudes by taking a simple Gaussian average over certain momentum variables. In effect, this gives a way of introducing focussing effects into strong-field QED calculations `for free'. The extension of these results to scattering amplitudes including only partial depletion is discussed and some first results presented in the anti-self-dual limit.

We apply the Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] to the two-dimensional Hubbard model, which is known to suffer from a severe sign problem when the system is doped (away from half filling). We show that the method predicts physical observables with controlled statistical errors on an $8 \times 8$ lattice at temperature $T/t = 1/6.4 \approx 0.156$ and interaction strength $U/t = 8.0$ ($t$ is the hopping amplitude), for which the standard determinant quantum Monte Carlo fails.

We investigate a scalar-vector-tensor theory in which matter is minimally coupled to a Jordan-frame metric, while a massive vector sector interacts with the baryonic current. We show that the conformal scalar coupling modifies the physical expansion rate measured by matter observers, leading to a late-time enhancement of the effective Hubble constant. By constructing a phenomenological scalar evolution that becomes relevant only at low redshifts, the model provides a purely late-time mechanism for alleviating the Hubble tension without significantly affecting early-universe cosmology. The scalar potential naturally acts as a dynamical dark-energy sector, while the vector contribution behaves effectively as a pressureless component at cosmological scales through a density-dependent vector mass. Hence, the framework connects late-time scalar dynamics, effective dark-energy evolution, and Hubble-tension alleviation within a unified setup. Finally, local gravitational constraints can be suppressed through a chameleon-type screening mechanism, allowing the theory to remain compatible with Solar-System tests while retaining nontrivial cosmological effects.

We point out that a simple late-time cosmological model where our Universe can absorb "baby universes" explains the exponential expansion of our universe without the need of a cosmological constant and leads to a z-dependence of the parameter w(z) in the equation of state. In this model w(z) is less than -1 for z sufficiently large.

We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit. This refines conventional notions of complexity beyond the linear circuit depth which is required to prepare any topological phase, and provides a new resource-theoretic characterization of topological orders. A central technical result is a no-go theorem establishing that stabilizer states--even up to constant-depth local unitarie--cannot approximate low-energy states of non-Abelian string-net models which satisfy the entanglement bootstrap axioms. Moreover, we show that stabilizer-realizable Abelian string-net phases have mutual braiding phases quantized by the on-site qudit dimension, and that any violation of this condition necessarily implies extensive long-range magic. Extending to higher spatial dimensions, we argue that any state obeying an entanglement area law and hosting excitations with nontrivial fusion spaces must exhibit extensive long-range magic. This applies, in particular, to ground-states and low-energy states of higher-dimensional quantum double models.

Using the post-Newtonian effective field theory (PN-EFT) formalism for spinning gravitating bodies, we derive the next-to-leading-order (NLO) spin-orbit potential and Hamiltonian for a system of N spinning bodies in general relativity. This extends the EFT treatment of the binary case to arbitrary N. We present two derivations: one in the generalized canonical gauge, and one based on the covariant spin supplementary condition (SSC), followed by a noncanonical transformation to canonical variables. In both approaches, the only new contributions beyond the binary case are three-body interaction diagrams. The canonical Hamiltonians obtained from the two EFT routes agree with the known ADM N-body Hamiltonian of Hartung and Steinhoff up to a canonical transformation.

A direct coupling between the inflaton and Standard Model gluons can dynamically raise the QCD confinement scale during inflation, making the axion temporarily heavy and suppressing axion isocurvature perturbations. As inflation proceeds, the confinement scale relaxes, the axion becomes light, and late-time de Sitter fluctuations can generate the observed dark matter abundance. We analyze this mechanism without specifying an inflationary potential, instead parametrizing the background by $\epsilon(N) \propto 1/N^p$, where $N$ is the number of $e$-folds before the end of inflation. The single parameter $p$ distinguishes monomial models ($p=1$), standard plateau models ($p=2$), and ultra-flat plateau or hilltop-like models ($p\ge 3$). We (analytically) show that the mechanism selects plateau-like ($p\ge 2$) inflation: monomial models generically cause the confinement scale to grow too rapidly, while plateau models keep the QCD sector under perturbative control. In the minimal scenario, reheating occurs through the same inflaton-gluon coupling, and viable axion dark matter production is obtained when deconfinement occurs after the CMB window. The early-confinement sector also shifts the scalar spectral index to larger, bluer values, opening viable parameter space for models otherwise disfavored by CMB data.

We investigate realizations of (1+1)-dimensional fusion category symmetries on tensor-product Hilbert spaces, allowing for mixing with quantum cellular automata (QCAs). It was argued recently that any such realizable symmetry must be weakly integral. We develop a systematic analysis of QCA-refined realizations of fusion categories and prove two statements. First, we show that, under certain physical assumptions on defects, any QCA-refined realization has QCA and symmetry-operator indices determined by the categorical data, up to the freedom of redefining the symmetry operators. Second, we construct a lattice model that provides a QCA-refined realization for any weakly integral fusion category symmetry on a tensor product Hilbert space. We also compute indices of the QCAs in our lattice model and show agreement with the first result. As an application of the general construction, we give an explicit QCA-refined realization of general Tambara-Yamagami categorical symmetries.

In a recent work, Ogawa et al. (2024) proposed a model for celestial conformal field theory (CFT) based on the $H_{3}^{+}$-Wess-Zumino-Novikov-Witten (WZNW) model. In this paper, we extend the model advanced by Ogawa et al. (2024), demonstrating how it can holographically generate tree-level MHV scattering amplitudes for both gluons and gravitons when analytically continued to the ultra-hyperbolic Klein space $\mathbf{R}_{2}^{2}$, thereby offering an alternative to celestial Liouville theory. We construct a holographic dictionary in which vertex operators and conformal primaries in celestial CFT are derived from their worldsheet counterparts in Euclidean $AdS_{3}$ (bosonic) string theory. Within this dictionary, we derive the celestial stress-energy tensor, compute the two- and three-point functions, and determine the celestial operator product expansion (OPE). Additionally, we derive a system of partial differential equations that characterises the celestial amplitudes of our model, utilising the Knizhnik--Zamolodchikov (KZ) equations and worldsheet Ward identities. In the Appendix, we provide a concise introduction to the $H_{3}^{+}$-WZNW model, with emphasis on its connection to Euclidean $AdS_{3}$ string theory.

A given topological manifold can sometimes be endowed with inequivalent differential structures. Physically this means that what is meant by a differentiable function (smooth) is simply different for observers using inequivalent differential structures. {The 7-sphere, $\bS^7$, was the first topological manifold where the possibility of inequivalent differential structures was discovered \cite{Milnor}.} In this paper, we examine the import of inequivalent differential structures on the physics of fields obeying the Dirac equation on $\bS^7$. { $\bS^7$ is a fibre bundle of the 3-sphere as a fibre on the 4-sphere as a base. We consider the Kaluza-Klein limit of such a fibre bundle which reduces to a SO(4) Yang-Mills gauge theory over $\bS^4$. We find, for certain specific symmetric set of gauge potentials, that the spectrum of the Dirac operator can be computed explicitly, for each choice of the differential structure. Hence identical topological manifolds have different physical laws. We find this the most important conclusion of our analysis.

We apply the background charged bosonic free-field approach to the rational principal quantum Drinfeld-Sokolov (QDS) $\mathcal{W} \big[ \widehat{g} \big](p,p')$ minimal models with boundaries, where $g$ is a finite bosonic simple Lie algebra. Their Ishibashi states are expressed using the free bosonic Ishibashi states, by applying the Fock space resolutions. The Coulomb-gas formalism is applied to the calculations of the disk two-point correlation functions in some well-studied and lesser familiar rational QDS $\mathcal{W} \big[ \widehat{g} \big](p,p')$ minimal models. The analytical expressions can be obtained by the repeated applications of the Pochhammer contour integral expression and the Taylor expansions of Lauricella's hypergeometric functions $F_{D}^{(n)}$.

Hilbert spaces in theories of gravity are notoriously subtle due to the Hamiltonian constraints, particularly regarding the inner product. To demystify this subject, we review and extend a collection of ideas in canonical gravity, and connect to the sum-over-histories approach by clarifying the Hilbert space interpretation of various gravitational path integrals. We use one-dimensional (or mini-superspace) models as the simplest context to exemplify the conceptual ideas. We emphasise that a physical Hilbert space can be defined either by requiring states to be annihilated by constraint operators (e.g., the Wheeler-DeWitt equation) or by equivalence relations between wavefunctions, and explain that these two approaches are related by an inner product. We advocate that the group averaging procedure constructs the correct physical inner product. The Klein-Gordon inner product is not positive-definite, which we explain as arising from a bad gauge choice; nonetheless, it agrees with group averaging when such a problem is absent. These concepts are all embedded in the BRST/BFV formalism, which provides a systematic way to construct these and other physically equivalent inner products (e.g., from maximal-volume gauge and Gaussian averaged gauges). Finally we discuss the application of these ideas in the semi-classical approximation, including non-perturbative gravitational effects.

It has recently been shown that the Nambu-Goto equation for a string emerges from the junction conditions in three-dimensional gravity. Holographically, gravitational junctions are dual to interfaces in conformal field theory. We demonstrate at the level of linearized gravitational perturbations that each stringy mode of the junction corresponds to a $\mathcal{H}_{in}\rightarrow \mathcal{H}_{out}$ quantum map which can be factorized into a scattering matrix involving reflection/transmission and a relative automorphism of the Virasoro algebra, and also a $\mathcal{H}_{L}\rightarrow \mathcal{H}_{R}$ map of similar nature. These maps preserve the conformal boundary condition, are independent of the background conformal frame, as in the case of conformal interfaces studied in the literature, and realize a tunable energy transmitter.

The Drude-Kadanoff-Martin model is a simple low energy and long wavelength description of charge transport, parameterised by the current relaxation timescale $\tau$, charge diffusivity $D$ and charge compressibility $\chi$. We obtain sharp constraints on these parameters in terms of the microscopic energy and length scales of any underlying lattice model with local and bounded interactions. Our primary tools are upper bounds on the retarded Green's function for the charge density in such a setting. We first note that the Drude-Kadanoff-Martin model cannot pertain at microscopic energy scales because it is inconsistent with the exponential suppression of spectral weight at the highest frequencies in a lattice model. Secondly, under the assumption that the low energy dynamics is captured by the model, we obtain a lower bound on the collective mean free path $\ell \equiv \sqrt{\tau D}$. This bound is shown to imply a version of the Mott-Ioffe-Regel bound: systems with $\ell$ much shorter than the lattice length scale cannot have conventional Drude peaks.

We demonstrate that $n$-way junctions in three dimensional gravity correspond to coupled $n-1$ strings each satisfying the Nambu-Goto equation in the smoothened background, and with sources consisting of Monge-Ampère like terms which couple the strings. For $n\geq 3$, these $n-1$ degrees of freedom survive the tensionless limit implying that matter-like behavior can arise out of \textit{pure} gravity. We interpret these stringy degrees of freedom of gravitational junctions holographically in terms of wavepackets which collectively undergo perfect reflection at the multi-interface in the dual conformal field theory.

Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev model (DSSYK). First, we demonstrate that the growth rate of Krylov state complexity corresponds to the wormhole velocity, and show that its expectation value in coherent states serves as a boundary diagnostic of firewall-like structures via bulk reconstruction. We also delineate an alternative bulk description in terms of the proper momentum of an infalling particle at early times, establishing a threefold duality between the Krylov complexity growth rate, wormhole velocity, and proper momentum, with clear regimes of validity. Beyond the first moments, we argue that higher-order Krylov complexities capture connected bulk contributions encoded by replica wormholes, while the logarithmic variant probes the replica saddle structure. Finally, within a third-quantized setting incorporating baby universes, we show that the Krylov entropy equals the von Neumann entropy of the parent-geometry density matrix obtained after tracing out baby universes, thereby quantifying information flow into the baby universe sector. Together, these results elevate Krylov-space observables to sharp probes of bulk dynamics and topology in ensemble-averaged 2D gravity.

This work, which accompanies [1], is about constructing smooth solutions in type II and eleven dimensional supergravity which describe supersymmetry preserving RG flows from four-dimensional SCFTs in the UV to three-dimensional SQFTs in the IR, through holography. We show that all the different UV fixed points flow to theories which confine external quarks and have a mass gap. We proceed by presenting extended calculations of a plethora of observables and analyse the dual field theories in great detail. This includes a boundary analysis and application of holographic renormalization methods in the simplest case of the type IIB solution. Many of the observables computed here have a universal behaviour: they factorize into two parts, one of which includes information about the UV SCFTs, and the other describing the dynamics of the RG flow, which is the same regardless of the UV fixed point.

We construct solutions of type-II supergravity based on multiple copies and/or mixings of $\lambda$-deformed coset CFTs on $\mathrm{SO}(n+1)_k/\mathrm{SO}(n)_k$, with $n = 2, 3, 4$. The resulting ten-dimensional geometries contain undeformed $\mathrm{AdS}$ factors, thereby allowing a connection between $\lambda$-deformations and the AdS/CFT correspondence. Imposing reality conditions on the solutions further constrains the deformation parameter. In some cases these bounds exclude the undeformed ($\lambda = 0$) or non-Abelian T-dual ($\lambda \to 1$) limits. This work extends the results of 1911.12371 and 2411.11086.

We study the coupling matrix of $\mathcal{N}=2$ $SU(N)$ gauge theories with $2N$ fundamental hypermultiplets in the special vacuum, where a residual $\mathbb{Z}_N$ symmetry restores nontrivial modular structure. Using symmetry and dimensional arguments, we construct its general form and identify $\lfloor N/2 \rfloor$ coupling constants in their most natural basis. We show that in the massless theory these couplings transform independently under $S$-duality and that the bare coupling is a modular function of any of them. One coupling constant, however, plays a distinguished role, emerging in the asymptotic regime and in instanton recursion relation. In the massive case, this structure is deformed but the distinguished coupling retains its privileged role.

We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the ultraviolet contributions. The method leads us to identify an apparent difficulty to renormalize with Hamiltonian counterterms within the in-in formalism. We also discuss the importance of the finite parts of loop corrections that can be distinguished from their associated counterterm contributions. As an application, we examine the one-loop primordial bispectrum in the context of the effective field theory of inflation, considering a specific set of interactions, and identifying a contribution distinguishable from its tree-level counterpart.

We explore the space of non-gravitational, maximally supersymmetric, planar 4d effective field theories (EFTs) that have $\mathcal{N}=4$ super Yang-Mills (SYM) at leading order. We show that in the weakly-coupled regime, highly non-trivial nonlinear constraints on the 4-point Wilson coefficients follow from enforcing $\mathcal{N}=4$ supersymmetry and $SU(4)$ R-symmetry together with the requirement of standard tree-level factorization on the massless poles of the 4-, 5-, and 6-point EFT scattering amplitudes. Additionally, when these novel constraints are combined with positivity, the resulting bounds on the 4-point Wilson coefficients converge to the values of the open string Veneziano amplitude. Our results strongly suggest that supersymmetry, R-symmetry, and positivity are sufficient to single out this unique UV completion at tree level. Our findings, moreover, highlight the power of higher-point amplitudes in constraining EFT data and imply that the space of consistent quantum field theories is even more restricted than previously suggested by causality or swampland-based approaches.

It has been proposed that any coupling constant in a covariant action can be treated as a conserved charge by promoting the coupling constant to auxiliary fields, typically realized by a scalar field paired with a higher-form gauge field. However, the procedure may break local symmetries, which can be explicitly shown in a simpler setting such as Maxwell theory. The Hamiltonian analysis of Maxwell theory with the auxiliary fields reveals that some of the constraints are second-class. Applying the BFT formalism, we restore the broken local symmetries and obtain a fully symmetric action defined on an extended configuration space. Despite the restoration of the local symmetries, no additional conserved charges are associated with the recovered symmetries. Consequently, the original theory turns out to be the gauge-fixed version of the extended theory.

Conservation of super-horizon tensor fluctuations is crucial for connecting inflation to observations. Starting from first principles, recent works have found violations of this conservation if free-streaming radiation is produced during reheating. We show that the non-conservation is sensitive to the radiation initial state, and argue that the physical state should be affected by tensor perturbations that are already present during reheating. The deviation from super-horizon conservation is then negligible, recovering the standard result from kinetic theory. In contrast, a globally homogeneous and isotropic plasma state leads to a large suppression of tensor amplitudes. This difference between the local (physical) and global thermal equilibrium settles the discrepancy between the older and recent literature.

Carrollian amplitudes are scattering amplitudes of massless particles written in position space at null infinity. We study various aspects of Carrollian amplitudes for gauge theory and gravity at loop level using primarily the modified Mellin prescription of [1]. Finite one-loop four-point Carrollian amplitudes in gauge theory are shown to maintain an analytic structure similar to tree level results. We compute the one-loop four-point Carrollian MHV amplitudes in planar $N=4$ super Yang-Mills theory, which are expressed as differential operators acting on tree level Carrollian amplitudes. This result is generalized to all loop orders using the Bern-Dixon-Smirnov (BDS) formula. Similar structures are observed at one-loop for Carrollian MHV amplitudes in $N=8$ supergravity. We next consider $2\to 2$ scattering of massless scalars via gravitational interactions in the eikonal regime and show that the corresponding Carrollian amplitudes exhibit logarithmic behavior in the `Carroll time' $u$. We compute the discontinuities of these Carrollian amplitudes up to $O(G^3)$ and show that they are descendants of Carrollian Born amplitudes. We observe similar logarithmic behavior in Carrollian amplitudes associated with the one-loop scalar box diagram. The dependence of this amplitude on dual scaling dimensions also differs from standard tree level results. Finally, we further study the infrared (IR) divergences of Carrollian amplitudes in massless scalar QED, gravity, and Yang-Mills theory. We show that Carrollian amplitudes in these theories naturally factorize, allowing us to provide an IR-safe definition for these objects.

We investigate the spreading of entanglement, and entanglement memory effects, in two-dimensional conformal field theory (CFT) propagating on evaporating black hole backgrounds. Memory effects leading to late-time spikes in mutual information for widely separated intervals are well known in CFTs admitting a quasiparticle description. In this work we examine the effect of black hole scrambling on late time mutual information spikes for disjoint intervals in free fermion CFT prepared in a thermofield double state. Late-time entanglement revival is driven by island-induced purification of modes in the union of the intervals. We show across two distinct 2d gravity models, Jackiw-Teitelboim (JT) gravity and the Russo-Susskind-Thorlacius (RST) model, that parametrically dialing up black hole scrambling time smooths out and suppresses entanglement spikes until they disappear at a critical scale, interpolating between free quasiparticle and maximal scrambling pictures. At the critical point, the interval lengths are exponential in black hole scrambling time. We further find a very closely related effect manifest as an entanglement dip for a single interval in a single-sided evaporating RST black hole.

We apply the complex scaling method to black-hole perturbations in four-dimensional Schwarzschild--de~Sitter (dS) spacetimes. The method converts the outgoing-wave boundary-value problem into a non-Hermitian spectral problem and enables quasinormal-mode poles and the rotated continuum to be treated in a common framework. We focus in particular on the continuum level density, which characterizes the continuum response beyond isolated quasinormal-mode frequencies. Using Regge--Wheeler-type perturbation equations for scalar, electromagnetic, and gravitational fields, we investigate how a nonzero cosmological constant modifies the pole and continuum sectors. We also discuss a possible extension to string-inspired coupled-channel systems, and illustrate that higher-dimensional dS black holes can be treated within the same framework, at least in tensor- and vector-type sectors. Our results indicate that complex scaling offers a useful spectral framework for analyzing both quasinormal modes and continuum response in black-hole physics.

Calculating the action and the interaction Hamiltonian at higher orders in cosmological perturbation theory is a cumbersome task. We employ the formalism of EFT of inflation in the decoupling limit for single-field ultra slow-roll (USR) inflation and obtain a non-perturbative Hamiltonian in terms of the Goldstone field $\pi$. To complete the dictionary, a non-linear relation between the curvature perturbations and $\pi$ is presented. Using these results, we compute higher-order loop corrections in USR models with a sharp transition to the attractor phase, relevant for PBHs formation. It is shown that in the idealized picture in which the transition from the USR phase to SR phase is instantaneous and sharp, the loop corrections on long CMB scales increase rapidly with the number of loops $L$ and the setup may go out of perturbative control.

We calculate the action and the interaction Hamiltonians to all orders in perturbation theory in the model of single field inflation with a transient ultra slow-roll phase. Employing the formalism of EFT of inflation, we obtain a compact non-perturbative expression for the interaction Hamiltonian in terms of the Goldstone field $\pi$ in the decoupling limit. In addition, we also present a non-linear relation between $\pi$ and the curvature perturbations to all orders in perturbation theory. These are powerful results which enable us to calculate the cosmological correlators and loop corrections to any order in perturbation theory. As a non-trivial example, we calculate the $L$-loop corrections on long CMB scale perturbations in the USR models which are used for PBHs formation. We show that the loop corrections scale like $(\Delta N {\cal P}_e L) ^L$ in which ${\cal P}_e$ is the peak of the power spectrum and $\Delta N$ is the duration of the USR phase. This indicates that the loop corrections grow quickly out of perturbative control for large values of $L$. In the conventional USR setup for PBHs formation with $\Delta N \simeq 2.5$, this happens at $L=4$.

The Minkowski vacuum is often presented in textbooks and reviews as a thermofield double (TFD) state, an entangled state of field modes in the left and right Rindler wedges. This picture is widely used to explain the Unruh effect, motivate entanglement entropy calculations, and connect quantum field theory to black hole thermodynamics and AdS/CFT. However, we show that this interpretation, while elegant, is not exact. We explicitly compute two-point functions and their derivatives for a massless scalar field in two-dimensional Minkowski space, comparing results obtained from canonical quantization with those obtained by assuming a TFD form of the vacuum. Mixed-derivative correlators agree perfectly, but higher-derivative correlators show systematic mismatches that persist even for points well away from horizons and are not removed by infrared regularization. To further test this picture, we construct an alternate coordinate system that divides Minkowski spacetime into two disconnected regions, apply the same derivation that leads to the standard TFD expression, and obtain a new "entangled-state" representation of the vacuum that is not thermal. This demonstrates that the appearance of a TFD structure is a feature of the derivation method rather than a fundamental property of the vacuum. Our results clarify the limits of interpreting the Minkowski vacuum as a literal TFD state, emphasizing that while it captures key thermal features, it should be viewed as a powerful calculational tool rather than a precise statement about Hilbert space structure.

The asymptotically flat, electrically charged, rotating black holes (BHs) in Einstein-Maxwell-dilaton (EMd) theory are known in closed form for \textit{only} two particular values of the dilaton coupling constant $\gamma$: the Einstein-Maxwell coupling ($\gamma=0$), corresponding to the Kerr-Newman (KN) solution, and the Kaluza-Klein coupling ($\gamma=\sqrt{3}$). Rotating solutions with arbitrary $\gamma$ are known only in the slow-rotation or weakly charged limits. In this work, we numerically construct such EMd BHs with arbitrary $\gamma$. We present an overview of the parameter space of the solutions for illustrative values of $\gamma$ together with a study of their basic properties. The solutions are in general KN-like; there are however, new features. The data suggest that the spinning solutions with $0<\gamma<\sqrt{3}$ possess a zero temperature limit, which, albeit regular in terms of curvature invariants, exhibits a $pp$-singularity. A different limiting behaviour is found for $\gamma>\sqrt{3}$, in which case, moreover, we have found hints of BH non-uniqueness for the same global charges.

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient algorithm for addressing the numerical sign problem at moderate computational cost. It mitigates the sign problem while avoiding the ergodicity issues inherent in approaches based on Lefschetz thimbles. In this study, we apply WV-HMC to the two-dimensional Hubbard model doped away from half filling, which is known to suffer from a severe sign problem. We compute the number density and the energy density on lattices of size $6 \times 6$ and $8 \times 8$ at temperature $T/t = 1/6.4 \simeq 0.156$ and interaction strength $U/t = 8.0$, using Trotter number $N_t = 20$ (Trotter step $\epsilon = 0.32$). Our results demonstrate that WV-HMC remains effective even in parameter regimes where standard (non-thimble) determinant quantum Monte Carlo methods fail. In this work, fermion matrix inversions are performed using direct solvers, leading to a computational cost of $O(N^3)$, where $N$ denotes the number of degrees of freedom and is proportional to the spacetime lattice volume. An alternative algorithm employing pseudofermions and iterative solvers, which reduces the cost to $O(N^2)$ at the expense of careful parameter tuning, will be discussed in a separate publication.

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient and versatile algorithm that mitigates the sign problem while resolving the ergodicity issues inherent in Lefschetz-thimble approaches. We focus on cases where the maximum flow time can be kept small, such as when applying WV-HMC to the doped Hubbard model utilizing a redundant, nonphysical parameter. An optimal choice of this parameter significantly reduces the sign problem on the original integration surface. This allows for small flow times, thereby enabling the simulation of larger system sizes at a modest computational cost. However, when the worldvolume reduces to a thin layer, phase-space exploration becomes inefficient, and ergodicity problems may reemerge. To address this limitation in WV-HMC, we propose embedding generalized thimble HMC (GT-HMC) into the WV-HMC framework. GT-HMC performs updates on a single deformed surface at a fixed flow time. Despite its inherent ergodicity issues at the zeros of the Boltzmann weight, GT-HMC efficiently explores the allowed region and typically permits larger molecular dynamics step sizes than WV-HMC. Consequently, it is highly effective in regions where ergodicity issues are less severe. We prove that GT-HMC can be consistently embedded within WV-HMC and confirm that the standalone and combined algorithms agree within statistical errors for the two-dimensional doped Hubbard model on an $8 \times 8$ lattice. This combined algorithm enables simulations on larger spacetime lattices. We demonstrate the feasibility of this approach by extrapolating the number and energy densities to the zero Trotter step limit at fixed temperature $T/t = 1/6.4\simeq 0.156$ and repulsive interaction $U/t = 8.0$. Even with modest sample sizes, we achieve controlled statistical errors across the entire range of the chemical potential.

We design a lattice model of a "mixed" U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations, For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics (QED$_3$) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, corresponding to a Zeeman field perturbing the Dirac spin liquid, we find a "chiral flux" phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. In this state, the U(1)$_m$ magnetic symmetry is spontaneously broken, leading to a gapless free photon mode which, due to spin-flux-attachment, is observable in the longitudinal spin structure factor. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.

The tidal deformation of compact objects, characterised by their Love numbers, provides insights into the internal structure of neutron stars and black holes. While static bosonic tidal Love numbers vanish for black holes in general relativity, it has been recently revealed that static fermionic tidal perturbations can induce non-zero Love numbers for Kerr black holes. In this paper, we investigate the response of the Reissner-Nordström black hole to the fermionic Weyl field. As a result, we find that the corresponding fermionic tidal Love numbers are also non-vanishing for the Reissner-Nordström black holes except for the extremal ones, which highlights the universal distinct behavior of the static fermionic tidal Love numbers compared to the bosonic counterparts.

We present the two-loop amplitudes for a self-dual Higgs boson with up to four positive helicity gluons in the heavy top-quark limit. Because the tree amplitudes in the all-plus sector vanish, we can construct simple representations of the polylogarithmic parts of the two-loop amplitudes using four-dimensional unitarity cuts into rational one-loop and tree amplitudes. The remaining rational function ambiguity is extracted from a tensor integral reduction over finite fields. The final expressions are presented using polylogarithms up to weight two and compact rational functions of spinor-helicity products.

We propose a general framework for the study of asymptotically flat spinning dyonic {\it extremal} black holes (eBHs) in $D=4$ Einstein-Maxwell-dilaton theory. Restricting to the stringy value $\gamma=1$ of the dilaton coupling constant, we report on the existence of a one parameter family of eBHs which are free of pathologies, provided their magnetic and electric charges are equal. An understanding of this condition is found from a study of the near horizon limit of the solutions, both perturbative closed form and numerical solutions being presented.

We investigate metric perturbations of a spherically symmetric black hole in higher curvature gravity. We show that higher curvature corrections deform the near-horizon region of the effective potential, and that the deviations of the quasinormal mode (QNM) frequencies from their general relativity (GR) values become more pronounced for overtone modes. We find that, as the order of the higher curvature term increases, the deformations approach the horizon and the deviations of the overtone QNM frequencies grow progressively larger. We also analyze the ringdown waveforms in the higher curvature gravity model. We consider setups in which the deviations from the vacuum-GR QNMs remain mild for the fundamental mode and the first few overtones, and show that these shifted QNMs can be identified in the ringdown signal through waveform fitting.

We formulate within Supergravity a model of induced-gravity inflation, excellently consistent with ACT DR6, inspired by the Palatini gravity. The inflaton belongs in the decomposition of a conjugate pair of Higgs superfields which lead to the spontaneous breaking of a U(1)B-L symmetry at a scale close to the range (0.102-5.85)x10^16 GeV. The inflaton field is canonically normalized thanks to a real and shift-symmetric contribution into the Kaehler potential. It also includes two separate holomorphic and antiholomorphic logarithmic terms, the argument of which can be interpreted as the coupling of the inflaton to the Ricci scalar. The attainment of inflation allows for subplanckian inflaton values and energy scales below the cut-off scale of the corresponding effective theory. Embedding the model in a B-L extension of the MSSM we show how the mu parameter can be generated and non-thermal leptogenesis can be successfully realized. An outcome of our scheme is split SUSY with gravitino mass in the range (40-60) PeV, which is consistent with the results of LHC on the Higgs boson mass.

Sign-switching dark energy provides a novel mechanism for modifying the late-time expansion history of the Universe without invoking additional fields or finely tuned initial conditions. In this work, we investigate a class of background--level cosmological models in which the dark energy contribution changes sign at a transition redshift $z_\dagger$, producing a sharp deviation from standard $\Lambda$CDM dynamics. We confront these models with a comprehensive set of cosmological observations, including Planck 18 cosmic microwave background (CMB) measurements, DESI DR2 Baryonic Acoustic Oscillation (BAO) data and the Pantheon+ $\&$ SH0ES Type Ia supernova sample (SN). Using a full Markov Chain Monte Carlo (MCMC) analysis, we find that the sign-switching scenario significantly alleviates the Hubble tension while obtaining better results when statistically comparing with $\Lambda$CDM, as quantified by the Akaike and Bayesian information Criteria. Although the model is explored only at the background level, the improvement in the inferred Hubble constant demonstrates that sign-switching dark energy offers a promising and physically economical pathway toward resolving late-universe discrepancies.

In this work we investigate the influence of weak acceleration on the confinement-deconfinement phase transition in gluodynamics. Our study is carried out within lattice simulation in the comoving reference frame of accelerated observer which is parameterized by the Rindler coordinates. We find that finite temperature confinement-deconfinement phase transition turns into spatial crossover in the Rindler spacetime. In other words, spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. We determine the position of the boundary between the phases as a function of temperature for several accelerations and find that it can be described by the Tolman-Ehrenfest law with rather good accuracy although a minor deviation takes place. Moreover, the critical temperature of the system in the weak acceleration regime is found to remain unchanged as that of the standard homogeneous gluodynamics. Our results imply that the spatial confinement-deconfinement transition might take place in the vicinity of the Schwarzschild black hole horizon.

Chaplygin gas and other k-essence models exhibit emergent geometry, with perturbations propagating on an acoustic metric disformally related to the Einstein-frame metric. For superluminal sound speed, we identify the disformal metric as the "causal frame," since choosing a finite causal-frame lapse yields hyperbolic equations of motion for fields propagating in either frame. We show that with a phantom Chaplygin gas, the Einstein-frame lapse is forced to pass smoothly through zero and change sign while the causal-frame lapse remains positive. As a result, Einstein-frame degrees of freedom (including the scale factor) undergo spontaneous time-reversal while the Chaplygin gas evolves monotonically, enforcing a robust non-singular bounce even in the presence of additional matter canonically coupled to the Einstein frame.

We develop the discrete set of Dyson-Schwinger equations for scalar fields and solve them for some cases. We show that their solutions are Gaussian in the continuum limit as expected from the theorems of Aizenman and of Aizenman and Duminil-Copin for $d\ge 4$. Extension to lower dimensionality fails, as it should, by observing that the triviality theorems used in our proof are not applicable in such cases.

Positive and negative flows of the Chen-Lee-Liu model and its various reductions, including Burgers hierarchy, are formulated within the framework of Riemann-Hilbert-Birkhoff decomposition with the constant grade two generator. Two classes of vacua, namely zero vacuum and constant non-zero vacuum can be realized within a centerless Heisenberg algebra. The tau functions for soliton solutions are obtained by a dressing method and vertex operators are constructed for both types of vacua. We are able to select and classify the soliton solutions in terms of the type of vertices involved. A judicious choice of vertices yields in a closed form a particular set of multi soliton solutions for the Burgers hierarchy. We develop and analyze a class of gauge-Bäcklund transformations that generate further multi soliton solutions from those obtained by dressing method by letting them interact with various integrable defects.

An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational interaction necessarily comes with some level of noise, i.e., non-reversibility. Here, we give a systematic classification of all possible such models consistent with the basic requirements that the non-relativistic limit is Galilean invariant and reproduces the Newtonian interaction on average. We demonstrate that for any such model to be non-entangling, a quantifiable, minimal amount of noise must be injected into any experimental system. Thus, measuring gravitating systems at noise levels below this threshold would be equivalent to demonstrating that Newtonian gravity is entangling. As concrete examples, we analyze our general predictions in a number of experimental setups, and test it on the classical-quantum gravity models of Oppenheim et al., as well as on a recent model of Newtonian gravity as an entropic force.

The paper develops a model to understand the effective quantum geometry of a black hole horizon and the emission of Hawking spectrum in $2+1$ dimensions. Using the algebra of Hamiltonian charges on the horizon, we establish that one should view the black hole horizon as formed out of quantised lengths of elementary quanta of value $8\pi \ell_{P}\, n$, where $n\in \mathbb{N}$, and $\ell_{P}$ is the Planck length. We determine the black hole entropy using this equidistant length spectrum in the microcanonical ensemble and show that its value is close to the Bekenstein-Hawking entropy. To evaluate the Hawking spectrum, we note that, to an observer near the black hole horizon, the entropy (or length of horizon cross-section) is related to the black hole energy. Hence, one may develop a formulation of length ensemble (similar to the area canonical ensemble of Krasnov) from which the black body spectrum may be obtained directly. This local observer perceives a Hawking spectrum whose temperature is modified by the Tolman factor.

We propose that the size of the universe and its rate of expansion cannot be simultaneously specified with arbitrary precision, a quantum mechanical statement encoded in a deformed commutation relation for the scale factor. The deformation modifies the Friedmann equation by adding a geometric correction to the expansion rate, and the sign and magnitude of a single free exponent determine the cosmological behavior. When the exponent is positive, the model predicts late-time dark energy with $w > -1$, testable with current and next-generation surveys. When the exponent is sufficiently negative, the same deformation produces a non-singular classical bounce that resolves the Big Bang singularity. The model introduces no new particles or fields and preserves a scale-invariant primordial power spectrum. The deformation has a natural interpretation as a horizon-scale phenomenon, with the cosmological horizon, and not the Planck length, setting its characteristic scale. The late-universe regime is then its generic application, with the expansion history as the primary observable signature. Cosmic acceleration may be the macroscopic imprint of quantum gravity at the cosmological horizon.

We explore the possibility of explaining dark matter through six-dimensional (6D) primordial black holes (PBHs) in a theory with two extra dimensions. Interestingly, in this scenario the fundamental energy scale is of the order of $\sim 10$ TeV, accessible by future experiments. We analyse the viability of charged and rotating 6D black holes under standard Hawking evaporation as well as the memory burden scenario. In the case of pure Hawking evaporation, only PBHs with masses $M > 10^8$ g survive to present, while the lifetime of near-extremal configurations is extended by a factor $1/\beta^{1/2}$, where the parameter $\beta$ characterizes small deviations from extremality. In the memory burden scenario evaporation is enormously suppressed, and sub-gram mass PBHs can survive to the present epoch. At future colliders such as the Future Circular Collider, these micro black holes produce characteristic high multiplicity events, $\langle N \rangle \sim 21$, with thermal spectra, enabling direct probes of the fundamental scale and the number of extra dimensions. We find that the memory burden mechanism opens a broad new mass window for light PBH dark matter, while the Kaluza-Klein mass splitting $\Delta m$ aligns with the atmospheric neutrino scale, suggesting a unified framework between Swampland constraints, cosmology, collider physics, and low energy phenomenology.

Schwarzschild black holes are expected to emerge as the end states of the classical gravitational collapse from non-singular configurations. After integrable curvature singularities appear, the interior geometry can be modelled to exhibit a transition, called ``Minkowski breaking'', when the inner horizon disappears, before all matter collapses into the central singularity. This picture implies a quantum framework to describe the final stages of the gravitational collapse, and here we will provide more insights from the semiclassical approximation for the energy-momentum tensor and the Madelung approximation for collapsing matter. In particular, we will show that the quantum potential in the Raychaudhuri equation starts to strongly oppose the collapse towards the Schwarzschild singularity precisely after the Minkowski breaking.

This dissertation presents a unified framework for medium characterization with hard probes spanning from Cherenkov light in quantum electrodynamics (QED) to jet drift in quantum chromodynamics (QCD). We first develop a dispersive fit to the refractive index $n(\lambda)$ of liquid argon (LAr) by incorporating anomalous dispersion at the 106.6 nm resonance for the first time. We show that the angular distribution of Cherenkov radiation is highly sensitive to the peak of the refractive index and contributes a significant excess over isotropic scintillation in certain angular bins. This work is important for precision Particle Identification (PID) for experiments like DUNE and CCM. Transitioning to high-energy nuclear collisions, we utilize ``jet drift'' -- the flow-induced deflection of partons -- as a tomographic probe of the Quark-Gluon Plasma (QGP). Using the Anisotropic Parton Evolution (APE) Monte Carlo simulation across various collision systems (PbPb, AuAu, and UU), we disentangle how the jet modification depends on medium size, temperature, and geometry. We show that jet drift exhibits distinct systematics in observables like the elliptic flow ($v_2$) and dihadron acoplanarity ($\Delta\phi$), which helps disentangle it from conventional energy loss. Together, these studies demonstrate how the angular and kinematic signatures of hard probes revolutionize our ability to resolve the fundamental properties of matter.

Understanding heat transport in low-dimensional and nano-architectured materials remains a central challenge in nonequilibrium statistical physics due to persistent deviations from Fourier's law. These deviations are driven by anharmonicity, reduced dimensionality, and the emergence of long-lived coherent excitations. In this work, we develop a unified theoretical framework for two-dimensional thermal metamaterials that combines nonlinear lattice dynamics, soliton-based effective field theories, and geometrically organized defect networks as guiding structures for energy flow. We introduce minimal discrete and continuum-inspired models suitable for controlled benchmarking of thermal transport in patterned two-dimensional architectures and identify a two-channel transport mechanism in which coherent nonlinear excitations coexist with incoherent hydrodynamic modes. The interplay between these channels is shown to be highly sensitive to geometry, nonlinearity, and temperature, offering new avenues for thermal management. We establish rigorous connections between microscopic nonlinearity, geometry-driven channeling of heat in two dimensions, and quantum-enabled exploration of both high-occupation classical regimes and genuinely quantum regimes beyond the reach of standard simulation strategies. The theoretical predictions are corroborated by recent experimental and computational results in Stone-Wales-defected PdSSe monolayers and silicon phononic crystal nanostructures, which exhibit ultra-low thermal conductivity coexisting with high carrier mobility and strong anisotropy -- direct manifestations of the two-channel mechanism. This synthesis provides actionable guidance for the design of engineered heat-spreading architectures and positions quantum simulation as a transformative tool for advancing the theory of nonlinear heat transport.

The inflationary Lyth bound relates the primordial tensor amplitude to the inflaton field excursion. There is no analogous universal relationship in the case of ekpyrotic, bouncing, and cyclic models because scalar and tensor perturbations depend on entropy conversion, matching through the bounce and the specific mechanism that violates or evades the null energy condition. Nevertheless, the background kinematics fulfills a useful non-inflationary analogue: a field-space distance budget. In this study, we propose a phase-resolved distance criterion for a non-inflationary smoothing process and decompose the invariant scalar distance into ekpyrotic smoothing, entropy-to-curvature conversion, bounce, and post-bounce contributions. Then, we impose BKL anisotropy suppression as an additional constraint on the ekpyrotic phase. In the canonical phase of the ekpyrotic contraction, we recover the known small-field scaling and generalize it to total budget inequality. We impose three requirements: a BKL (Belinski-Khalatnikov-Lifshitz) anisotropy suppression that is parameterized separately, a phenomenological cutoff-corrected distance budget inspired by tower of states logic, and observational conversion windows from residual isocurvature and non-Gaussianity. Furthermore, we propose a new master condition that provides a lower bound on the value of the parameter $\epsilon_{\rm ek}$ that depends on the remaining distance available after conversion and the cosmological bounce. We also derive a curvature constraint for scale-invariant entropy perturbations in curved field space which shows that the small total distance and the observed red tilt seem to indicate ultra-fast-roll ekpyrosis, sharp turns, short or strongly modified bounces, and/or significant negative sectional curvature of the scalar manifold. Finally, we demonstrate methods for testing the distance budget against observational data.