Using the worldline quantum field theory formalism, we compute the conservative scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian (5PM) order by providing the second self-force (2SF) contributions. This four-loop calculation involves non-planar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at $v/c=\sqrt{8}/3$. This divergence is present in the potential region and must be cancelled by conservative memory contributions from radiative regions. We find that the standard use of Feynman propagators to access the conservative sector fails to ensure this cancellation. We propose a conservative propagator prescription which realises both cancellations leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.

Gapped two-dimensional gauge theories with massless fermions generically have rich vacuum structures consisting of many degenerate vacua related by the action of topological line operators. The algebra of such operators has been used to calculate ratios of vacuum expectation values of local operators and to predict nontrivial particle-soliton degeneracies. In this paper, we use recently-developed tensor network methods to study several examples of such theories via their Hamiltonian lattice descriptions. Our lattice results agree with all previously-made predictions. Furthermore, we identify the lattice strong-coupling states that can be adiabatically continued to the degenerate vacua in the continuum limit. We conjecture a procedure, referred to as a lattice decay rule, for how this identification works in general. This rule allows us to compute the continuum vacuum degeneracy by studying the lattice Hamiltonian in the strong-coupling limit.

We develop a systematic approach to the computation of gauge invariant quartic interactions between reducible massive and massless higher spin fields. Extending the BRST formulation of existing cubic results, we obtain a single constraint for each off-shell quartic vertex that ensures both the gauge invariance of the Lagrangian and associativity of the gauge transformations at quartic order. A solution to these equations is presented. The general equation is then reduced to an on-shell version to reduce complexity. We find example solutions for the off-shell and on-shell quartic vertices in low spin examples relevant to the problem of black hole scattering.

We reexamine the energy-momentum tensor in classical electrodynamics from the perspective of spacetime-dependent translations, i.e., diffeomorphism invariance in flat spacetime. When energy-momentum is identified through local translations rather than constant ones, a unique, symmetric, and gauge-invariant energy-momentum tensor emerges that satisfies a genuine off shell Noether identity without invoking the equations of motion. For the free electromagnetic field, this tensor coincides with the familiar Belinfante-Rosenfeld and Bessel-Hagen expressions, but arises here directly from spacetime-dependent translation symmetry rather than from improvement procedures or compensating gauge transformations. In interacting classical electrodynamics, comprising a point charge coupled to the electromagnetic field, diffeomorphism invariance yields well-defined energy-momentum tensors for the field and the particle, while the interaction term itself generates no independent local energy-momentum tensor. Its role is instead entirely encoded in the coupled equations of motion governing energy-momentum exchange, thereby resolving ambiguities in energy-momentum localization present in canonical and improvement-based approaches.

We investigate integrable boundary states in the anisotropic Heisenberg chain under periodic or twisted boundary conditions, for both even and odd system lengths. Our work demonstrates that the concept of integrable boundary states can be readily generalized. For the XXZ spin chain, we present a set of factorized integrable boundary states using the KT-relation, and these states are also applicable to the XYZ chain. It is shown that a specific set of eigenstates of the transfer matrix can be selected by each boundary state, resulting in an explicit selection rule for the Bethe roots.

Fundamental scale invariance implies the scale invariant standard model. Both the Fermi scale and the Planck mass are given by fields, and their ratio is dictated by a dimensionless cosmon-Higgs coupling. For an ultraviolet fixed point of quantum gravity this coupling is an irrelevant parameter of the renormalization flow and becomes predictable. An analytic scaling solution for quantum gravity admits no free parameter for the mass term of the Higgs boson. If the largest intrinsic mass scale generated by the renormalisation flow away from the fixed point is sufficiently below the Fermi scale, the couplings of the scale invariant standard model are determined by the scaling solution. For a given short distance model remaining valid to infinitely small distances the ratio Fermi scale over Planck mass can be predicted. With reasonable assumptions for an ultraviolet fixed point a numerical solution finds a tiny value for the ratio between the Fermi and Planck scales, very close to a second order quantum electroweak phase transition. This could explain the observed gauge hierarchy.

The Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) construction encodes all the data of a topological sigma-model in the finite-dimensional symplectic $Q$-manifold. Relaxing the nondegeneracy condition i.e. considering a presymplectic form instead, extends the construction to non-topological models. The gauge-invariant action functional of (presymplectic) AKSZ sigma model is written in terms of space-time differential forms and can be seen as a covariant multidimensional analogue of the usual 1st order Hamiltonian action. In this work, we show that the AKSZ construction has a natural generalisation where the target space $Q$-manifold is equipped with a form of arbitrary degree $\Omega$ (possibly inhomogeneous) which is $(\mathrm{d}+L_Q)$-closed. This data defines a higher-derivative generalisation of the AKSZ action which is still invariant under the natural gauge transformations determined by $Q$ and which is efficiently formulated in terms of a version of Chern-Weil map introduced by Kotov and Strobl. It turns out that a variety of interesting gauge theories, including higher-dimensional Chern-Simons theory, MacDowell-Mansouri-Stelle-West action and self-dual gravity as well as its higher spin extension, can be concisely reformulated as such multisymplectic AKSZ models. We also present a version of the construction in the setup of PDE geometry and demonstrate that the counterpart of the multisymplectic AKSZ action is precisely the standard multisymplectic formulation, where the Chern-Weil map corresponds to the usual pullback map.

We investigate whether the hidden zeros and associated factorisations found for massless colour-ordered amplitudes persist under massive deformations. Using the kinematic mesh construction, we show that hidden zeros survive only for symmetry controlled mass generation. For massive $\text{Tr} \Phi^3$ with a uniform mass, the zeros and their factorisation patterns are inherited after a massive shift of planar variables, and an analogous statement holds for Kaluza-Klein reductions where the relevant non-planar variables are modified by conserved mode numbers. For the non-linear sigma model (NLSM), a naive pion mass term generically spoils hidden zeros, while a spurion induced potential restores them. This allows factorisation near zeros, including odd point channels described by an appropriately mass deformed NLSM + $\phi^3$ theory, and leads to a hidden zero based on-shell recursion for massive NLSM amplitudes. For spin-one, a simple massive Yang-Mills theory fails to exhibit hidden zeros, while spontaneously broken gauge theories preserve them.

Motivated by recent results in spin chains we study dissipation and relaxation in a two-dimensional holographic interface conformal field theory (ICFT) in which degrees of freedom on one side of the interface are coupled to an external bath, while the other side remains isolated. In the bulk description this setup is realized by gluing a supersymmetric Janus geometry to a BTZ black hole region, with the coupling implemented through a double-trace deformation. We determine the quasinormal modes in the bulk by solving the double-trace matching conditions of the system and bath. The lowest imaginary part of the modes defines a Liouvillian gap, and following earlier work in spin chains we introduce the dimensionless ratio crelax as a measure of interface-induced suppression of relaxation. Numerically we find that, crelax is independent of coupling details to the bath. It is a strong candidate for a universal interface observable characterizing dissipation and relaxation across the interface.

Supergravity theories in de Sitter spacetime are known to be very constrained, and rather unnatural within String/M Theory. We revisit the seminal paper by Pilch, van Nieuwenhuizen and Sohnius, where the possible existence of a real Lagrangian for ${\cal N}=2$ pure supergravity in four-dimensional de Sitter spacetime was pointed out. We clarify several issues related to the non-unitarity of the theory and explicitly construct the unique, complete theory searched for long ago by the aforementioned authors. We argue that the lack of unitarity of the Lorentzian theory may be revisited in the Euclidean approach to de Sitter quantum gravity, where alternative definitions of unitarity can be introduced.

Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space-time by means of a generalized microcanonical ensemble similar to the one of the standard microcanonical approach to lattice field theory. In a previous paper we showed that, for an interacting scalar field theory in 1+1-dimensions, this formalism allows to capture numerically some crucial real-time features inaccessible to any Euclidean approach to lattice field theory. Yet, the new approach was plagued by two main limitations: an ill-defined non-interacting limit and the absence of a direct formal correspondence between its correlation functions and those generated by the Feynman path integral approach. In this paper, we introduce the new \emph{"constrained symplectic quantization"} approach, for which the perfect equivalence with the Feynman path integral is proved and which is perfectly well defined for the free theory. This new approach is characterized by the analytical continuation of all fields and of the action from $\mathbb{R}$ to $\mathbb{C}$ and the presence of some constraints which guarantee the stability of the generalized Hamiltonian dynamics and the convergence of the corresponding generalized microcanonical partition function, hence the name of the theory. We show the application of this formalism to the quantum harmonic oscillator on a Minkowskian-time lattice, finding perfect agreement between one- and two-point numerical correlators and the exact quantum-mechanical results. We observe genuine real-time features such as the oscillatory propagator and the discrete excited-state energy spectrum. Our results provide strong numerical evidence that constrained symplectic quantization can sample real-time quantum-mechanical observables, offering a concrete route to overcome the limitations of Euclidean-time importance sampling.

Generalised axion-like scalar fields provide a well-motivated framework for describing the late-time acceleration of the Universe. As the field evolves, it rolls down its potential and, depending on its mass and initial conditions, it may either still be approaching the minimum or already oscillating around it. These two dynamical regimes require distinct treatments of cosmological perturbations. In this work, we perform a detailed analysis of linear cosmological perturbations in the regime where the dark-energy scalar field undergoes coherent oscillations about the minimum of its potential. We show that the standard effective fluid description breaks down in this phase and develop a consistent field-based perturbation framework, which we use to assess the impact of oscillatory dark energy on the growth of cosmic structures.

In four-dimensional vacuum general relativity the only known static, exact and analytical black hole solution is given by the Schwarzschild spacetime. In this paper this renowned metric is generalised by adding another integrating constant, a hair that switches the metric from the Petrov type D to the type I. This new parameter represents the intensity of an external gravitational field, which can be considered the hyperbolic generalisation of the Witten's bubble of nothing. No curvature or conical singularities are present outside the event horizon. The no hair arguments are circumvented because the metric is not asymptotically flat, and neither the black hole is spherical. The gravitational hair continuously deforms the Schwarzschild geometry: the horizon becomes oblate, while its area is reduced. Conserved charges and thermodynamic properties of the black hole are studied.

In this work, we present a theoretical analysis of null geodesics, critical photon orbits, and shadow formation associated with a wormhole generated by a geometric defect. The propagation of light in this spacetime is examined through the deflection angle in both weak- and strong-field regimes. Analytical expansions are derived in each regime and employed to characterize gravitational lensing observables. By varying the global monopole charge, we evaluate its impact on these observables and determine parameter ranges that may be accessible to current or future observational probes. Finally, we calculate the quasinormal modes as well as the time-domain solution for scalar perturbations as well.

We develop a general canonical quantization scheme for $k$-essence cosmology in scalar-tensor theory. Utilizing the Dirac-Bergmann algorithm, we construct the Hamiltonian associated with the cosmological field equations and identify the first- and second-class constraints. The introduction of appropriate canonically conjugate variables with respect to Dirac brackets, allows for the canonical quantization of the model. In these new variables, the Hamiltonian constraint reduces to a quadratic function with no potential term. Its quantum realization leads to a Wheeler-DeWitt equation reminiscent of the massless Klein-Gordon case. As an illustrative example, we consider the action of a tachyonic field and investigate the conditions under which a phantom crossing can occur as a quantum tunneling effect. For the simplified constant potential case, we investigate the consequences of different boundary conditions on the singularity avoidance and to the mean expansion rate.

Higgs boson pair production in the massless quark-antiquark channel proceeds at leading order (LO) via electroweak boson loops. We calculate the next-to-leading order QCD corrections to this process. For the corresponding two-loop amplitudes, an analytic representation has been achieved. Even though the size of this contribution at the level of total cross sections is below 1% compared to the LO gluon channel, the effect on differential observables can be in the 10% range and therefore this contribution should be taken into account when comparing to LHC data.

We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the $\mathbb{Z}_2$-orbifold of the $c=1$ compactified boson boundary conformal field theory, we construct microscopic lattice boundary terms that renormalize to the stable conformal boundary conditions,, utilizing simple current extensions and the underlying $\mathrm{SU}(2)$ symmetry to explicitly characterize the four-state Potts point. We validate these theoretical identifications via finite-size spectroscopy of the lattice energy spectra, confirming their consistency with $D_4$ symmetry and Kramers-Wannier duality. Finally, we discuss the boundary renormalization group flows among these identified fixed points to propose a global phase diagram for the boundary criticality.

In nonperturbative formulation of Euclidean signature quantum field theory (QFT), the vacuum state is characterized by the Wilsonian renormalization group (RG) flow of Feynman measures. Such an RG flow is a family of Feynman measures on the space of ultraviolet (UV) regularized fields, linked by the Wilsonian renormalization group equation. In this paper we show that under mild conditions, a Wilsonian RG flow of Feynman measures extending to arbitrary regularization strengths has a factorization property: there exists an ultimate Feynman measure (UV limit) on the distribution sense fields, such that the regularized instances in the flow are obtained from this UV limit via taking the marginal measure against the regulator. Existence theorems on the flow and UV limit of the corresponding action functional are also discussed.

We calculate the large-$N$ expansion of the sphere free energy $F=-\log Z_{S^d}$ of the O(N) $\phi^4$ and the Gross-Neveu $(\bar{\psi} \psi)^2$ CFTs to order $1/N$. Analytic regularization of these theories requires consistently shifting the UV scaling dimension of the auxiliary field: this can only be done by modifying its kinetic term. This modification combines with the counterterms to give the result that matches the $\epsilon$-expansion, resolving a puzzle raised by Tarnopolsky in arXiv:1609.09113. These $F$s can be written compactly in terms of the anomalous dimensions, for both the short-range and the long-range versions of these CFTs. We also provide various technical results including a computation of the counterterms on the sphere and a neat derivation of the sphere free energy of a free conformal field. Finally, we observe that the long-range CFT becomes the short-range CFT at exactly the point where its $\tilde{F} =-\sin \tfrac{\pi d}{2} F$ is maximized as a function of the vector's scaling dimension.

We propose a new way to relate the black hole thermodynamics and geometry by generalizing the Euclidean formalism to include "virtual geometries", which do not necessarily satisfy Einstein equations. This provides a physically well motivated route to study black hole criticality and obtain the Landau Ginzburg potential. We compute the "virtual thermodynamic potential" and show that it satisfies a modified quantum statistical relation that is compatible with the first law of black hole thermodynamics supplemented with an extra term, interpreted as virtual work in previous literature. The novelty is that, within our formalism, we can explicitly compute this term as the first derivative of the virtual thermodynamic potential with respect to the horizon radius that is considered as the order parameter. Imposing the physical condition that the first derivative vanishes is at the basis of the matching between the first law of black hole thermodynamics and (one of the) Einstein equations evaluated at the horizon. Interestingly, imposing the physical conditions that the second and third derivatives vanish, we can concretely study the criticality and existence of swallow tails. As a specific example, we apply this formalism to an exact four dimensional asymptotically flat hairy black hole, namely the generalized Kaluza Klein (KK) black hole when the dilaton potential is included, and show that it is thermodynamically stable and has a non-trivial critical behaviour corresponding to an inverted swallowtail.

We present a derivation of the first curvature correction to the AdS Veneziano amplitude for arbitrary Kaluza-Klein (KK) modes, using a bootstrap approach based on the world-sheet representation and AdS$\times$S formalism. Our results establish a universal formula for the first order curvature correction without considering any low-lying KK configurations. We give new predictions for Wilson coefficients in the low-energy expansion. In the high-energy regime, the amplitude exhibits a universal exponent independent of the external KK charges, providing a coherent picture of AdS stringy amplitudes in different backgrounds.

We present a fully analytic treatment of Schwarzschild--de~Sitter (SdS) black-hole evaporation in two-dimensional dilaton gravity with anomaly-induced backreaction. Starting from the spherical reduction of four-dimensional Einstein gravity with a cosmological constant, we construct an exactly solvable 2D model that captures the full causal and thermodynamic structure of the SdS static patch, including both black-hole and cosmological horizons. Incorporating the trace anomaly of $N$ conformal matter fields via the Polyakov action, we determine the evolution of the black-hole mass and geometry in the Unruh--de~Sitter state, track the steady nonequilibrium Hawking flux, and compute local thermodynamic observables for static observers. The conserved Killing energy flux drives an irreversible heat current from the black hole to the cosmological horizon whenever their surface gravities differ, ensuring monotonic entropy growth and satisfaction of the generalized second law. We prove that $\kappa_b>\kappa_c$ throughout the physical static patch, so the only zero-flux configuration is the Nariai limit where the horizons coincide. Extending the framework to the quantum-information regime, we construct a thermo-controlled estimate of the Page curve and show how quantum extremal surfaces and entanglement islands emerge naturally within the anomaly-induced steady state. These results constitute a fully analytic, backreacted solution for SdS evaporation that unifies semiclassical thermodynamics and information flow in a cosmological setting, thereby elucidating the ultimate fate of evaporating black holes in de~Sitter space.

We analyse a class of SYK models whose Hamiltonian is the sum of two SYK Hamiltonians with different numbers of fermions $q, \tilde q$ in each interaction. We consider both Euclidean and Lorentzian probes of the quantum system in the large $N$ limit. In the strong coupling phase, the entropy provides a diagnostic of the thermal renormalisation group flow. Under certain conditions, two parametrically separated regimes of near-conformal behaviour emerge. The first reproduces the standard linear-in-temperature scaling characteristic of the single SYK model. The system then flows to another near-fixed point whose entropy scaling depends on the ratio $n = q/\tilde q$. For $n<3/2$, the entropy exhibits anomalous, stronger-than-linear scaling in temperature. At $n=3/2$, there is an additional logarithmic enhancement. Using conformal perturbation theory, we argue that in the infrared regime of the SYK model, there may exist disordered conformal operators with dimensions $1 < \Delta \leq 3/2$. In Lorentzian signature, we study the out-of-time-ordered correlator and show that these deformed theories exhibit near-maximal chaos in both regimes (when they exist). We comment on the relation between the anomalous scalings found here and those observed in certain near-extremal black holes in two and higher dimensions.

In de Sitter (dS) holography, both the dS/CFT correspondence and the dS static patch holography have been extensively studied. In these two holographic frameworks, the dual field theories are defined on spacelike and timelike boundaries, respectively, where the inward motion of the holographic boundary into the bulk corresponds to the $T\bar{T}$ and $T\bar{T}+\Lambda_2$ deformations in the respective dual field theories. In this work, we develop a unified framework for these two dS holographic models by introducing a composite flow that incorporates both $T\bar{T}$ and $T\bar{T}+\Lambda_2$ deformations. We propose that this composite flow corresponds to the inward motion of a spacelike boundary from the asymptotic infinity of dS spacetime, traversing the cosmological horizon and approaching the worldline of a static observer. This proposal is supported by the computation of the quasi-local energy and the holographic entanglement entropy within the dS static spacetime and its extened geometry.

In 2507.17558, we provide a map from a scalar theory on $(D+2)$-dimensional Minkowski spacetime to a scalar theory with a continuous mass spectrum on $(D+1)$-dimensional de Sitter spacetime, and propose a link between celestial amplitudes and cosmological correlators (the cosmological-celestial dictionary). We extend the construction to fields with spin 1 and 2, and find that massless spin fields map to spin fields with continuous mass spectra. In this construction, we identify the de Sitter counterparts of the Nambu-Goldstone modes associated with the asymptotic symmetries in Minkowski spacetime. For $U(1)$ gauge theories, the counterpart is restricted to the massless sector within the continuous Proca spectrum, while for linearized gravity supertranslations are encoded in the partially massless sector and superrotations in the strictly massless sector. Using the identification, we reveal that the associated Ward-Takahashi identities of the cosmological correlators reproduce the conformally soft photon and graviton theorems via the cosmological-celestial dictionary. In particular, the celestial stress tensor is derived from the asymptotic limit of gravitons in de Sitter spacetime.

We investigate the analytic structure of thermal spectral function of holographic CFTs, synthesizing recent developments into a set of observations about its asymptotics. Specifically, for a class of scalar primaries with integral dimension, we demonstrate factorization of the exact spectral function into a polynomial piece, which captures the vacuum dynamics, and a non-perturbative piece, which controls its asymptotics. Using exact WKB techniques, we derive a transseries expression for the latter. We use this information to deduce the singular loci of a spatially averaged thermofield double correlator in the complex time plane. Such singularities have been argued to encode information regarding the black hole singularity in the dual spacetime. Our results give a refinement of these statements by capturing the momentum dependence.

We give an explicit closed form description of the late-time near-horizon approach to dynamical extreme Reissner-Nordstrom (DERN) black holes. These are spherically symmetric dynamical solutions of Einstein-Maxwell theory coupled to a neutral scalar that feature: (i) a spacetime metric which tends to that of a static extreme Reissner-Nordstrom (RN), and (ii) a scalar field which exhibits the linear Aretakis instability ad infinitum in the non-linear theory. We employ the two-dimensional Jackiw-Teitelboim (JT) gravity to solve explicitly for the non-linear s-wave dynamics of the four-dimensional theory near an ${\rm AdS}_2\times {\rm S}^2$ throat. For a teleologically defined black hole horizon, we impose boundary conditions on JT's dilaton field (which encodes the gravitational dynamics) and the scalar matter as follows: (i) the JT dilaton decays at late times on the ${\rm AdS}_2$ boundary to a value that corresponds to a static extreme RN in the exterior, and (ii) the scalar obeys boundary conditions characteristic of linear Aretakis behavior on ${\rm AdS}_2$. We ensure our DERN solutions are singularity-free and we note that our approach to DERN is accompanied by a final burst of outgoing scalar matter flux leaking out of the ${\rm AdS}_2$ throat. The boundary conditions we impose on the JT dilaton place its late-time boundary profile on the threshold of black hole formation with sub-extreme and super-extreme RN on either side of our DERNs.

We establish a precise formula relating the world-sheet integral of the AdS Virasoro-Shapiro amplitude to the energy-energy correlator (EEC) in $\mathcal{N}=4$ super Yang-Mills theory at strong coupling. This mapping allows us to evaluate the coefficients of the AdS curvature expansion of the EEC in terms of the world-sheet integral over a unit disk. To illustrate this idea, we explicitly compute the flat-space contribution and the first curvature correction to the EEC. Our results provide a rigorous description of the stringy energy flow, demonstrating how world-sheet correlator imprint themselves on collider observables and offering a potential template for effective string descriptions of energy correlators in general gauge theories.

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.

The surface charges associated with $p$-form gauge fields in the Bondi patch of $D$-dimensional Minkowski spacetime are computed. We show that, under the Hodge duality between the field strengths of the dual formulations, electric-like charges for $p$-forms are mapped to magnetic-like charges for the dual $q$-forms, with $q=D-p-2$. We observe that the complex combination of electric-like and magnetic-like charges transforms under duality according to a specific Möbius transformation. This leads to a possible construction of CCFT in $D=4$ as a Möbius-principal equivariant bundle, together with its associated bundles, in order to recover celestial operators. We prove an existence and uniqueness theorem for the duality map relating the asymptotic electric-like charges of the dual descriptions, and we provide an algebraic-topological interpretation of this map. As a result, the duality map has a topological nature and ensures that the charge of one formulation contains information about the dual formulation, leading to a deeper understanding of gauge theories, the non-trivial charges associated with them, and the duality of their observables. Moreover, we propose a link between higher-form symmetry charges, naturally associated with a $p$-form gauge theory, and their asymptotic charges. The higher-form charges are reproduced by choosing the gauge parameter to be constant and supported only on an appropriate codimension submanifold. This could partially answer an open question in the celestial holography program.

Parton distribution functions (PDFs) describe the inner, non-perturbative structure of hadrons. Their computation involves matrix elements with a Wilson line along a direction on the light cone, posing significant challenges in Euclidean lattice calculations, where the time direction is not directly accessible. We propose implementing the light-front Wilson line within the Hamiltonian formalism using tensor network techniques. The approach is demonstrated in the massive Schwinger model (quantum electrodynamics in 1+1 dimensions), a toy model that shares key features with quantum chromodynamics. We present accurate continuum results for the fermion PDF of the vector meson at varying fermion masses, obtained from first-principle calculations directly in Minkowski space. Our strategy also provides a useful path for quantum simulations and quantum computing.

We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic computational tool Cadabra. We present the linearized version of the equations of motion, performing the longitudinal-transverse decomposition. We compare the linear equations with the covariant field equations, finding that, if general-relativity terms are active, the linear Hamiltonian formulation is valid only if the perturbative spatial metric is traceless, a condition that can be freely imposed by recurring to an arbitrary function. We apply the equations of motion on homogeneous and isotropic configurations, finding explicit solutions.

In light of the recent results from the Atacama Cosmology Telescope (ACT), which have provided a notable shift in the constraints on $(n_s, r)$ and placed several otherwise viable models of inflation in tension with the latest data, we investigate the possible effects that radiative corrections can have on $\xi$-attractor and $\alpha$-attractor models of inflation. These models, which share much in common with Starobinsky inflation, have likewise been put under pressure by these results. We find that percent (and even sub-percent) level radiative corrections can easily shift both of these classes of inflation models comfortably into the regions of parameter space favoured by the most recent constraints. However, the flexibility under such corrections calls into question to what extent it is possible to precisely pin down model-specific predictions for important cosmological observables.

We investigate the impact of higher-order fermionic deformations in multiflavor Bardeen-Cooper-Schrieffer (BCS) theory. Focusing specifically on the 6- and 8-fermion interactions, we show that these terms can have significant consequences on the dynamics of the system. In certain regions of parameter space, the theory continues to exhibit second-order phase transitions with mean-field critical exponents and the same critical temperature; however, the temperature dependence of the superconducting gap can deviate markedly from conventional BCS behavior. In other regions, the theory exhibits first-order phase transitions or second-order phase transitions with non-mean field exponents. We conclude by discussing potential phenomenological applications of these theories.

Inflation with an inflection point potential is a popular model for producing primordial black holes. The potential near the inflection point is approximately flat, with a local maximum next to a local minimum, prone to eternal inflation. We show that a sufficient condition for eternal inflation is $\lambda_1 \leq 3$, where $\lambda_1$ is the index of the `exponential tail,' the lowest eigenvalue of the Fokker--Planck equation over a bounded region. We write $\lambda_1$ in terms of the model parameters for linear and quadratic regions. Wide quadratic regions inflate eternally if the second slow-roll parameter $\eta_V \geq -6$. We test example models from the literature and show this condition is satisfied; we argue eternal inflation is difficult to avoid in inflection point PBH models. Eternally inflating regions correspond to type II perturbations and form baby universes, hidden behind black hole horizons. These baby universes are inhomogeneous on large scales and dominate the multiverse's total volume. We argue that, if volume weighting is used, eternal inflation makes inflection point primordial black hole models incompatible with large-scale structure observations.

In this work, we introduce a novel framework to investigate ringdown gravitational waveforms in the presence of dynamical matter fields outside the horizon of a black hole. We systematically analyze two distinct scenarios of dynamical matter fields: motion along geodesics and uniform motion with constant velocity. Our results reveal rich phenomenology in the ringdown gravitational wave signals, including the suppression or enhancement of echoes, frequency shifts in the decay oscillations, and intricate modulations of the power-law tails. Notably, we demonstrate that subluminal moving potentials can produce irregular echo patterns and shift the dominant frequencies, offering potential new observational signatures beyond the already-known ringdown analyses. This study provides a new perspective for probing dynamic environments around black holes and offers a theoretical foundation for interpreting possible deviations in future gravitational wave detections.

Understanding the nature of dark matter (DM) particles remains a pivotal challenge in modern cosmology. Current cosmological research on these phenomena primarily utilizes cosmic microwave background (CMB) observations and other late-time probes, which predominantly focus on large scales. We introduce a novel probe, the 21 cm forest signal, which can be used to investigate DM properties on small scales during the epoch of reionization, thereby addressing the gap left by other cosmological probes. Annihilation and decay of DM particles, as well as Hawking radiation from PBHs, can heat the intergalactic medium (IGM). This heating suppresses the amplitude of the 21 cm forest 1D power spectrum. Therefore, the 1D power spectrum provides an effective method for constraining DM properties. However, astrophysical heating processes in the early universe can also affect the 21 cm forest 1D power spectrum. In this work, we assess the potential of using the SKA to observe the 21 cm forest 1D power spectrum for constraining DM properties, under the assumption that astrophysical heating can be constrained reliably by other independent probes. Under low astrophysical heating conditions, the 1D power spectrum could constrain the DM annihilation cross section and decay lifetime to $\langle\sigma v\rangle \sim {10^{-31}}\,{\rm cm^{3}\,s^{-1}}$ and $\tau \sim {10^{30}}\,{\rm s}$ for ${10}\,{\rm GeV}$ DM particles, and probe PBHs with masses $\sim {10^{15}}\,{\rm\,g}$ at abundances $f_{\mathrm{PBH}} \simeq 10^{-13}$. These constraints represent improvements of 5-6 orders of magnitude over current limits. Furthermore, the 21 cm forest 1D power spectrum has the potential to exceed existing bounds on sub-GeV DM and to probe PBHs with masses above $10^{18}\,{\rm g}$, which are otherwise inaccessible by conventional cosmological probes.

Extended Higgs sectors are often introduced to explain phenomena beyond the standard model (BSM). The existence of multiple scalar fields may cause the Landau pole below the Planck scale. In this case, the low-energy theory may be replaced by an asymptotic-free gauge theory. In this paper, we consider an $\mathrm{SU}(2)$ gauge theory with confinement as such an ultraviolet theory of the extended Higgs sectors. We investigate the relation between scalar particle contents at the low energy and group theoretical properties of fundamental fermions of the gauge theory. We find that particle contents of various extended Higgs sectors previously proposed to explain the BSM problems are deduced by each charge assignment of flavor symmetry of the fundamental fermions of the $\mathrm{SU}(2)$ gauge symmetry. Our findings may provide a new picture for the ultraviolet completion of the extended Higgs sectors.

We apply Lie symmetry analysis of partial differential equations (PDEs) to the Euler-Lagrange equations of the two-Higgs-doublet model (2HDM), to determine its scalar Lie point symmetries. A Lie point symmetry is a structure-preserving transformation of the spacetime variables and the fields of the model, which is also continuous and connected to the identity. Symmetries of PDEs may, in general, be divided into strict variational, divergence and non-variational symmetries, where the first two are collectively referred to as variational symmetries. Variational symmetries are usually preserved under quantization, and variational Lie symmetries yield conservation laws. We demonstrate that there are no scalar Lie point divergence symmetries or non-variational Lie point symmetries in the 2HDM, and re-derive its well-known strict variational Lie point symmetries, thus confirming the consistency of our implementation of Lie's method. Moreover, we prove three general results that may simplify Lie symmetry calculations for a wide class of particle physics models. Lie symmetry analysis of PDEs is broadly applicable for determining Lie symmetries. As demonstrated in this work, the method can be applied to models with many variables, parameters, and reparametrization freedom, while any missing discrete symmetries can be identified through the automorphism groups of the resulting Lie symmetry algebras.

We consider the transverse momentum ($q_T$) distribution of neutral charged bosons at hadron colliders. We perform the resummation of the logarithmically-enhanced effects due to simultaneous QCD and QED initial-state radiation, up to mixed next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of such mixed QCD$\otimes$QED resummed contributions on top of pure QCD corrections, finding percent-level effects.

We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the familiar setting of fusion categories, which describe finite group symmetries, to the case of Lie group symmetries. Within this framework, we obtain a functorial Symmetry Topological Field Theory together with its natural boundaries, allowing us to compute associated endomorphism categories and Drinfeld centers in a uniform way. For a given symmetry group $G$, our framework recovers the electric and magnetic higher-form symmetries expected in $G$-gauge theory. Moreover, it naturally encodes electric breaking symmetry in the presence of charged matter, reproducing known physical phenomena in a categorical setting.

We calculate the Feynman propagator at finite temperature in an Einstein universe for a neutral massive scalar field arbitrarily coupled to the Ricci curvature. Then, the propagator is used to determine the mean square fluctuation, the internal energy, and pressure of a scalar blackbody radiation as functions of the curvature coupling parameter $\xi$. By studying thermodynamics of massless scalar fields, we show that the only value of $\xi$ consistent with stable thermodynamic equilibrium at all temperatures and for all radii of the universe is $1/6$, i.e., corresponding to the conformal coupling. Moreover, if electromagnetic and neutrino radiations are present at the regime of high temperatures and/or large radii, we show that at least one scalar field must also be present to ensure thermodynamic stability.