We develop the boundary and celestial interpretation of finite Carrollian black-hole thermodynamics. The bulk input is the phase-space contraction of the time generator and Newton constant for which the extended AdS first law has a finite Carrollian limit. We show that this finite first-law line has a holographic interpretation as a double-scaled low-temperature, large-$N$ ensemble: the Carrollian temperature decreases while the effective number of boundary degrees of freedom grows, leaving the thermodynamic products in the first law finite. The large-$N$ dictionary is anchored by the standard $\mathrm{AdS}_5/\mathrm{CFT}_4$ normalization of adjoint degrees of freedom and by the Brown--Henneaux central charge in $\mathrm{AdS}_3/\mathrm{CFT}_2$. We construct the finite Carrollian Brown--York stress tensor on the contracted AdS boundary and show that its global energy charge is the finite bulk Hamiltonian. We then derive the boundary form of the first law in terms of the spatial volume and the holographic degree-of-freedom normalization. This identifies the Hawking--Page locus with the zero of the chemical potential conjugate to the count of degrees of freedom. The same charge is the global Carrollian supertranslation charge, so the finite first law is the thermal zero-mode sector of the Carrollian Ward identity. Finally, we construct the celestial conformal-primary representation of thermal Carrollian correlators. The finite celestial-basis correlators are rescaled double-scaled correlators obtained by combining the Fourier--Mellin transform with the rescaled thermal frequency window.

We review the representations of so(1,D), the algebra of isometries of D dimensional de Sitter space. We cover the representations in all D, including mixed symmetry representations and fermionic representations, and connect them to the various types of fields that can propagate on de Sitter space. The presentation is from a physics point of view, favoring concrete constructions over abstract considerations.

We give a formula for conserved charges in an arbitrary Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The formula is expressed in terms of the theory's $L_\infty$ data alone, without reference to the derivative structure of the Lagrangian. Therefore conserved charges can be computed in nonlocal models, such as string field theory, where conventional methods break down. We also show that the formula correctly expresses the surface charge of general relativity in terms of the Brown-York stress tensor. Related computations in Yang-Mills theory suggest that spatial boundaries are dealt with in a natural fashion.

What is the density of states of the de Sitter static patch? We propose a definition and calculation of such a density in 3d dS. Our proposal involves a sum over an SL(2,$\mathbb{Z}$) set of Euclidean no-boundary Kerr-lens spacetimes sourced by a line-defect with given energy and spin - which in Lorentzian time represents an observer's worldline at the center of the dS static patch. We develop an exact quantum computation of the spectral density using a holographic duality between dS$_3$ gravity and two copies of $\mathbb{C}$LS, the complex Liouville string. The SL(2,$\mathbb{Z}$) Kerr-lens spacetimes map under the duality to an SL(2,$\mathbb{Z}$) family of generalized crosscap geometries. We compute the $\mathbb{C}$LS $\otimes$ $\mathbb{C}$LS crosscap amplitudes and show that they match the semi-classical gravity prediction. For the simplest non-trivial Kerr-lens space, the $\mathbb{C}$LS $\otimes$ $\mathbb{C}$LS description is, in turn, dual to two copies of the $G\Sigma$ effective field theory of the double scaled SYK model. The $G\Sigma\otimes G\Sigma$ theory lives on an observer's worldline in the static patch, setting the stage for developing a microscopic worldline hologram of 3d de Sitter.

We present new charged and rotating near-horizon geometries in five-dimensional Einstein-Maxwell theory in closed analytic form. The solutions can be parametrised by the charge and two independent angular momenta. We also generalise these near-horizon geometries to theories with an additional Chern-Simons term in the action multiplied by an arbitrary coupling constant. The new solutions have the same entropy relations as expected for charged versions of extremal Myers-Perry black holes and for rotating versions of extremal Reissner-Nordström-Tangherlini black holes, but they do not reduce to the Myers-Perry horizon in the vacuum limit. The horizon cross-sections are spherical and carry a Sasakian structure. We exploit this structure to prove a characterisation of our solutions: without any symmetry assumptions, they are the most general rotating extremal horizons for which the co-rotating electric field is a (non-zero) constant. We further extend this construction to higher dimensions, where we show that any Sasaki-Einstein manifold generates a two-parameter family of charged and rotating horizons.

We study the closed-string tachyon and doubled Ramond-Ramond sector of type 0A in light of the proposed M-theory description on $S^1\vee S^1$-the wedge of two circles joined at a point. In this picture the two RR copies are associated with the two circle components, which we call branches, and tachyon condensation corresponds to shrinking one branch to the type IIA endpoint. From the type 0A equations of motion, we derive the branch-balance condition for a tachyon stationary point and identify the branch-odd RR fluctuation that sources the tachyon around a symmetric background. We then analyze the fate of the collapsing branch RR data as one branch of the wedge collapses to the type IIA endpoint. For an isolated unscreened collapsing-branch $D_p^-$ source, a Gauss-law estimate shows that the long-range RR field-energy cost scales inversely with the shrinking circle and thus becoming infinitely costly, generalizing the $D0^-$-brane decoupling in the original wedge picture. We describe the infrared screening of the relative RR field through an effective higher-form Stückelberg mechanism and distinguish this from a possible discharge of localized relative charge. Finally, using standard Wess-Zumino couplings of D-branes, we identify an effective relative-charge carrier and derive a parametric thin-wall criterion for when such a discharge channel $D_p^- \to D_p^+$ can be energetically favored.

We consider Yang--Mills, Chalmers--Siegel and self-dual Yang--Mills (SDYM) theories within AdS/CFT correspondence. Bulk-to-bulk and boundary-to-bulk propagators are derived in various gauges and for Dirichlet, Neumann, mixed and self-dual boundary conditions. Three- and four-point holographic correlators are computed in the three theories to establish the relation between the observables thereof. This is a companion paper to [arXiv:2602.21658].

We generalize the "holar wind" mechanism proposed in arXiv:2303.00234 to the case of rotating $\lambda$-deformed BTZ black holes. These backgrounds, which interpolate between $AdS_3$ in the infrared and a linear dilaton spacetime in the ultraviolet, are realized as an exact $\frac{SL(2,\mathbb{R})_k\times U(1)}{U(1)}$ gauged-WZW worldsheet theory. The long string sector of the theory provides a holographic dual to single-trace $T\overline{T}$ deformed symmetric product $\mathcal{M}^p/S_p$ $CFT_2$ with a seed $\mathcal{M}$ carrying a central charge $c=6k$. By analyzing the geodesics and tunneling rates of probe particles and winding long strings, we show that the emission probabilities for both positive and negative deformation couplings are universally governed by the change in the Bekenstein-Hawking entropy, $\Delta S_{BH}$. A central result of our analysis is that the consistency of long string emission within the grand canonical ensemble dictates a unique value for the background B-field at the origin. We demonstrate that this thermodynamically fixed value matches precisely the prediction required for the string excitation spectrum to agree with the $\mathbb{Z}_w$ twisted sector of a single-trace $T\overline{T}$ deformed symmetric product orbifold. Finally, we sketch the extension of these results to a broader class of black holes whose long string sector is dual to single-trace $T\overline{T} + J\overline{T} + T\overline{J}$ deformed theories.

In this paper we construct duality-covariant worldvolume dynamics of particles and branes. We extend known actions and phase space formulations to include the hidden $E_8$ symmetry of 11D supergravity, analogous to the Ehlers symmetry of 4D gravity. Making the worldvolume theory manifestly duality-covariant requires the ancillary structure of $E_8$ exceptional field theory to be taken into account. For zero-branes, we propose an enlarged worldline model with a coadjoint orbit term to encode this. More generally, we propose worldvolume theories for arbitrary exotic branes in a way that generalises the known gauged sigma model of the Kaluza-Klein monopole. These are natural in the duality-covariant Hamiltonian formulation employed here. We discuss the case of zero-branes in eleven dimensions as an illustrative example.

We investigate holographically dual descriptions of $(2+1)$-dimensional s-wave and p-wave superconductors in the framework of regularized four-dimensional Einstein-Lovelock gravity theories, incorporating higher curvature corrections beyond the Gauss-Bonnet sector. We first implement the 4D regularization of Einstein-Lovelock gravity with finely tuned coupling constants to include corrections up to any $K$th order in curvature. The bulk geometry is constructed from exact black-brane solutions characterized by the fine-tuned Lovelock coupling $\alpha$ and the highest power of curvature in the Lagrangian K. We then analyze the condensation of scalar and vector operators dual to minimally coupled matter fields, focusing on two bulk-field mass prescriptions, which significantly affect the superconducting phase. Our results demonstrate that higher curvature terms significantly modify the phase structure of both s-wave and p-wave systems and enhance the sensitivity of the condensates and critical temperatures to the gravitational couplings. In both cases, the critical temperature generally increases with the maximal curvature order K, leading to higher-$T_c$ phases compared to Einstein gravity, particularly for negative $\alpha$. The coupling $\alpha$ effectively governs the strength of higher curvature interactions in the bulk: positive $\alpha$ suppresses condensation and lowers $T_c$, whereas negative $\alpha$ enhances superconducting order and promotes higher-$T_c$ phases relative to Einstein gravity. We further study the optical conductivity and find that both the gap frequency and the ratio $\omega_g/T_c$ exhibit a strong dependence on $\alpha$ and $K$, deviating from the universal Einstein-gravity result. Higher curvature effects enhance the superconducting gap scale. Notably, the p-wave system shows a stronger sensitivity to the mass-fixing prescription compared to the s-wave case.

We compute the leading-order $1/N$ corrections to the central charges $C_J$ and $C_T$ in the conformal QED$_d$-Gross-Neveu-Yukawa (GNY) model and the scalar QED$_d$ in $d$ dimensions. The scaling dimensions of the lowest adjoint bilinear scalars are obtained to order $O(1/N)$ for general $d$. In $d=3$, the $U(1)$ Abelian gauge theory possesses a topological $U(1)$ global symmetry, and we evaluate the central charge $C_J^{\text{top}}$ of the topological symmetry current to subleading order in the $1/N$ expansion. Our interest in these theories is primarily motivated by their potential connection to the $SO(5)$ symmetric deconfined quantum critical point (DQCP). We compare the large $N$ results for the central charges $C_J$ and $C_T$ with the conformal data of the $SO(5)$ DQCP obtained from fuzzy sphere and conformal bootstrap. The large $N$ predictions of the QED$_3$-GNY model are found to be in reasonable agreement with the nonperturbative estimates for the $SO(5)$ DQCP.

Triangulations, i.e., well-structured decompositions of geometric objects into triangle-like pieces, are central objects in many domains of mathematics and physics. In particular, fine, regular, and star triangulations (FRSTs) of 4D reflexive polytopes give rise to smooth Calabi-Yau threefolds, which are of significant interest in string theory. However, the high dimensionality and combinatorial complexity of triangulations make them particularly challenging to model with classical numerical methods or machine learning. In this work, we show that transformers, equipped with an appropriate encoding scheme, can be effectively trained to representatively generate new FRSTs across a range of polytope sizes. Moreover, these models can also self-improve through retraining on their own output. This opens the door to both concrete applications to the classification of Calabi-Yau manifolds and further research in physics, combinatorics and algebraic geometry.

Computing Ricci-flat metrics on Calabi-Yau manifolds is challenging since no closed-form solutions are known. However, these computations are needed in order to make physical predictions in heterotic string theory, such as the masses of quarks and Yukawa couplings. In this manuscript, we present an overview of relevant literature for learning about Calabi-Yau manifolds, as ML researchers often face a steep learning curve when entering the field. Furthermore, we survey the impact of the manifold's symmetries on machine learning approximations to these flat metrics. We also characterise the isometries of Ricci-flat metrics, a result frequently omitted or used without proof. Then, we address symmetry breaking in point sampling and introduce a novel formula for computing volume ratios on general CICY manifolds. We conclude by presenting a new symmetry-aware model built using graph neural networks that avoids pathological behaviour witnessed in some other models.

The double copy of form factors has revealed a striking feature: poles that are spurious from the gauge-theory perspective become physical propagators in gravity. At the same time, form factors obey hidden factorization relations on the kinematics of these poles. We explain both phenomena by introducing a dyeing procedure, which promotes the color-singlet operator, or the Higgs particle representing it, to an adjoint massive state. The original form factor is recovered by the inverse bleaching operation, realized as a $U(1)$ decoupling of the dyed leg. In the dyed theory, these apparent spurious poles turn into ordinary physical propagators of colored amplitudes, and the hidden factorization relations follow from standard BCJ relations. Applying this framework to multiple operator insertions gives a systematic double-copy construction for multi-Higgs amplitudes and, as a byproduct, reveals scalar-ordering sectors. We also discuss higher-length scalar operators and fermionic operators, including the dyed vector construction for $\bar{\psi}\gamma^{\mu}\psi$, as well as a loop-level example.

Biadjoint scalar theory has been widely studied, due to its being closely related to the double copy correspondence linking gauge, gravity and related theories. In this paper, we continue a programme of work in elucidating non-linear solutions of this theory, and find a family of new solutions that are richer and more complex than previous cases. Using an ansatz that can be embedded in any choice of non-abelian colour groups, we demonstrate the existence of non-topological solitons, whose existence is protected by carrying a U(1) charge associated with certain rotations in colour space. The solutions are time-dependent, and closely related to the well-known Q-ball solutions in other scalar field theories. We also show explicitly that our solution set contains those that are stable under small perturbations within a consistent truncation of the theory, and have finite energy in addition to being localised.

Boruch, Emparan, Iliesiu, and Murthy recently discussed index saddles for 5d black strings, showing that the black string saddle admits a decoupling limit to a complex, finite-temperature BTZ \times S^2 saddle that computes the index of the dual CFT. In this paper, we pursue an analogous construction for the D1-D5-P black string. We construct a four-charge index saddle in the four-dimensional STU model as the BPS limit of the non-extremal four-charge black hole, and show that it exhibits the new form of attraction. We then uplift it successively to five and six dimensions, via the 4D-5D connection and a chain of string dualities, to obtain the gravitational index saddle for the D1-D5-P black string. We take a systematic decoupling limit of this index saddle and obtain the BTZ \times S^3 saddle that computes the index of the D1-D5 CFT.

We present two novel approaches for the numerical evaluation of Feynman integrals based on their universal analytic properties related to positivity, namely complete monotonicity (CM) and Stieltjes properties. Building on recent results, we exploit the fact that scalar Feynman integrals in the Euclidean region are completely monotonic functions, meaning that all their derivatives have a fixed sign. Building on this observation, the CM bootstrap allows one to reconstruct integrals from differential equations without explicit boundary data, yielding rigorous bounds. The second method is based on a refinement of CM. We prove that Feynman integrals, within a certain range of parameters, are not only CM but in fact Stieltjes functions. This enables the use of Padé approximants with provable convergence properties in the cut complex plane, providing an efficient method for analytic continuation and fast numerical evaluation. We illustrate the method with simple examples such as the massive bubble integral and discuss applications to multi-loop integrals, including the 20-loop banana integral. Finally, we comment on a number of extensions of these novel avenues for computing Feynman integrals.

We study the gauge invariance of different continuum methods to include non-perturbative effects in gauge theories. We work with three dimensional quantum electrodynamics and implement vertices using two different methods: a set of coupled Schwinger-Dyson (SD) integral equations, and the self-consistent equations obtained from the 3-particle irreducible (3PI) effective action. We work in Landau gauge and assess the extent to which results are gauge invariant by checking how well the Ward identity is satisfied. Our results show that there is a fairly significant violation of the Ward identity at large coupling, although the 3PI effective theory is slightly better than the SD vertex. We also compare the results of both calculations with the commonly used Ball-Chiu ansatz and show that the agreement of the ansatz with both non-perturbative vertices is fairly good at small coupling but deviates more significantly at large coupling. We compare results for the two point functions of the theory and discuss the possible implications for phase transitions.

Recently, it was proposed that the leading high-energy behavior of scattering amplitudes is universal, independent of charge, thereby extending the equivalence principle beyond the graviton pole. In this Letter, we derive a sharper causality constraint on such behavior by studying the Regge limit of colored scattering. Parameterizing a trajectory by $s^{\alpha(t)}$ with $\alpha(0)=2-\delta$, we analyze the Shapiro/Wigner--Smith time-delays in the irreducible scattering channels. We show that any non-singlet trajectory with $\delta< 1/2$ produces a growing sign-indefinite time-delay (with $\delta=1/2$ a marginal, dimension-dependent case), which becomes dominant in the Regge diffusion region in the weak-gravity regime. The essential point is that, while the eikonal phase is naturally organized in $t$-channel irreducible representations, the physical time-delays are its eigenvalues in the $s$-channel. A non-singlet exchange therefore recouples into the physical channels with both signs, inevitably producing a negative time-delay in at least one channel.

The SO(1,3)-symmetric reduction of Yang-Mills theory on Minkowski space yields a stress-energy tensor that is smooth on the timelike and spacelike Lorentz orbits but diverges on the lightcone that separates the two regions. We ask what consistent source this singularity represents. A natural cure is a real shift of the singular denominator. This does not regularize the source but instead moves the singular support onto a hyperboloid off the cone, where the corresponding source cannot remain both conserved and traceless. Our analysis shows that the displaced support cannot retain both properties, whereas a completion on the lightcone can. The matching condition fixes this completion up to one parameter $\chi$, which has a causal interpretation as the relative weight of the future and past cones. On regular constant-time slices, the completed source carries zero total four-momentum, so its physical content is a residual causal charge inferred from its curvature response.

A remarkable universality appears in the low-temperature quantum thermodynamics of near-extremal black holes, where distinct parent geometries often lead to the same logarithmic temperature dependence at one loop. In this work, we study the Lichnerowicz spectral origin of this infrared universality and understand why the relevant spectral data become insensitive to the details of the parent geometry. For extremal near-horizon geometries containing a two-dimensional maximally symmetric throat, we construct the normalizable transverse-traceless tensor zero modes associated with near-horizon reparametrizations. Turning on a small temperature lifts these zero modes through the first-order deformation of the Lichnerowicz operator. Although the local matrix element depends on detailed parent-geometry data, these data cancel after projection onto normalized tensor modes, leaving the universal result. For static spherically symmetric backgrounds, the eigenvalue shift is universally proportional to the Fourier mode number and temperature, and the same structure persists for rotating backgrounds, where angular warp factors only modify the overall projection factor. We further show that this lifted bulk spectrum is the Lichnerowicz realization of the Schwarzian soft sector. Thus, the universal first-order result is traced to an infrared bulk-boundary matching between near-horizon tensor zero modes and boundary reparametrization dynamics.

Deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave. A Laplace transform turns this fact into a general method: it resolves each curved-space mode into a superposition of plane waves dressed by a kernel that encodes the spacetime geometry, field content and dynamics, collapsing the time integrals onto flat-space ones. This provides simple diagrammatic rules that turn cosmological correlator diagrams into their flat-space counterparts integrated against Laplace-space kernels. On the paradigmatic massive single exchange, this integral representation makes the energy singularities manifest and evaluates in closed form as a single, rapidly convergent series valid throughout the kinematic domain, with no patching of separate expansions. The Laplace approach sheds conceptual and computational light on cosmological correlators in virtually any theory of the early universe.

We develop a new approach to cosmological correlators, built on a simple physical fact: deep inside the Hubble radius every mode oscillates as a flat-space plane wave, the curvature of spacetime making itself felt only as the mode is stretched towards the horizon. A Laplace transform turns this observation into a computational tool, resolving each curved-space mode function into a continuous superposition of plane waves labelled by a dual variable and dressed by a kernel that encodes the spacetime geometry, field content and dynamics. Every time integral then reduces to an elementary flat-space one, yielding simple diagrammatic rules for cosmological correlators. We illustrate the construction on the massive single-exchange correlator. The Laplace representation makes its total- and partial-energy singularities transparent ''from flat space'', and yields a single closed-form, rapidly convergent series valid throughout the entire kinematic domain. Although developed for conformally coupled fields exchanging massive scalars in de Sitter, the approach carries over essentially unchanged to virtually all situations of interest in primordial cosmology.

Supergravity solutions describing stacks of D$p$-branes with $p\neq 3$ feature a non-constant dilaton profile, which is holographically mapped to the running of the SYM coupling in $(p+1)$ dimensions. For D-instantons ($p=-1$), the lack of space and time in the IKKT matrix model makes such an interpretation difficult at first. In this letter, we propose a method to achieve this based on two closely related concepts: the IKKT method of integrating out heavy strings in a Coulomb branch vacuum and the matrix RG flow of Brézin and Zinn-Justin (BZJ). The notable difference between the two is that the BZJ RG flow also integrates over the Coulomb branch position. We first apply the Coulomb branch method and by relating the coefficient of the leading correction to the IKKT action with the string coupling, we can compute its dependence on the Coulomb branch position, finding a match between matrix theory and supergravity. Next, we apply the BZJ-flow to the IKKT partition function, which leads to a running of the coupling constant $g$ with the rank $N$ of the matrix model, reproducing the $N$-dependence of the axio-dilaton field in supergravity.

We develop a geometric interpretation of Schwinger--Dyson identities by showing that their violations are controlled by a single score-mismatch field $\delta s$. For an arbitrary sampled probability distribution $Q$ and equilibrium measure $P_{\rm eq}$, every Schwinger--Dyson violation is determined by $\delta s = \nabla \log (Q / P_{\rm eq})$, which characterizes the departure from equilibrium. Each Schwinger--Dyson identity measures a projection of this field onto a probe direction in configuration space. The relative Fisher information is its squared norm. This gives a universal bound relating Fisher information to the complete Schwinger--Dyson hierarchy, thus implying that convergence in Fisher information restores all Schwinger--Dyson identities. We further obtain a variational characterization of the relative Fisher information in terms of Schwinger--Dyson violations, leading to a natural tomographic interpretation in which increasingly rich families of probe fields encode progressively more information about the underlying probability distortion. The configurational temperature, within this framework, emerges as a distinguished Schwinger--Dyson probe. The Stein operators and score-function methods arise naturally from the same probability-geometric structure. The score-mismatch field, therefore, provides a unified geometric language for understanding Schwinger--Dyson identities, configurational temperature, Fisher information, and non-equilibrium sampling in stochastic processes.

Inspired by the string theory, the braneworld picture introduces extra dimensions beyond the four that may have observable non-trivial effects in short distance (strong field) gravity experiments. A case in point is the Randall-Sundrum braneworld picture that projects the $5d$ bulk Weyl tensor onto the $3d$ brane providing a stress tensor in the effective Einstein field equations on the brane. Dadhich, Maartens, Papadopoulos and Rezania (DMPR) derived an exact braneworld black hole solution of the brane vacuum field equations. The solution formally resembles that of Reissner-Nordström but is physically different from it since the "tidal charge" $\Upsilon$ in the solution is not the electric charge but an imprint from the fifth dimension allowing both signs in the power law modification $\pm \frac{\Upsilon ^{2}}{r^{2}}$ to the Schwarzschild metric $\left( \Upsilon = 0\right)$. The corresponding black holes are designated as DMPR$\pm$. We study here the effect of $\Upsilon$ on strong field lensing observables and compare in the eikonal limit the ring down quasinormal mode (QNM) frequencies of DMPR$-$ with those of DMPR$+$, the two variants of tidal charge modified Schwarzschild black hole ($\Upsilon = 0$). It turns out that the tidal charge can significantly modify the Schwarzschild lensing observables and QNM frequencies. In particular, we find that the Pretorius-Khurana critical exponent $\gamma$ of circular null orbits in the DMPR$-$ black hole has a lower value than that for the Schwarzschild black hole, which indicates a stronger Lyapunov instability suggesting that the accretion disks of DMPR$-$ black holes would appear brighter. The case of the SgrA* black hole is considered for a possible constraint on $\Upsilon$ from the EHT observation of its shadow size.

Horizon-scale imaging acts as a transformative tool for probing spacetime geometry, enabling stringent tests of gravitational theories in the strong-field regime. The Casadio-Fabbri-Mazzacurati(CFM) black hole in braneworld contains an extra parameter that characterizes the tidal effects from the bulk geometry, making it highly valuable for this task. We perform general relativistic radiative transfer (GRRT) simulations and generate synthetic images consistent with Event Horizon Telescope observations of M87*. We find that the tidal parameter imprints nonmonotonic changes on the image morphology, underscoring the intricate coupling between spacetime geometry and the observable radiation from the accreting plasma. We also analyze the image-comparison metric using normalized cross-correlation coefficients and the DSSIM index and find that the magnitudes of these mismatches are on the order of 10^3, which implies that identifying braneworld black holes through black hole images remains challenging even with future ngEHT and BHEX observations.

We construct an exact solution for the electrically charged extension of a distorted black hole spacetime within Einstein-Maxwell theory using the Harrison transformation. The resulting solution represents a charged deformation of a static distorted vacuum geometry in which the electromagnetic field is introduced through a nonlinear transformation preserving the radial structure of the seed spacetime. Consequently, the Killing horizon remains determined solely by the seed metric and it is not shifted by the electric charge. We analyze the thermodynamic properties of the solution and show that the horizon area, entropy, and temperature are governed by the geometric sector, while the electric charge enlarges the thermodynamic phase space through the electromagnetic potential. The motion of charged test particles is studied using the effective potential formalism, where the distortion parameter modifies circular orbits and shifts the location of the innermost stable circular orbit. We also investigate the black hole shadow for a static observer at finite distance and show that the distortion parameter displaces the photon sphere outward, increasing the apparent shadow size. A geometric correspondence between the photon orbit, determining the shadow and the leading eikonal quasinormal-mode frequency, is discussed, linking optical and perturbative observables. Finally, we study charged scalar perturbations and show that the vanishing horizon electric potential prevents a charged superradiant amplification. In the weak-coupling regime, the quasinormal-mode spectrum is estimated using the WKB method, where the electromagnetic interaction enters through the gauge-invariant combination $(\omega - q_s \xi_t)$ and shifts the oscillation frequencies of the perturbations.

We investigate the extended thermodynamics, including the Joule-Thomson expansion and $P-V$ criticality, of a four-dimensional charged anti-de Sitter (AdS) black hole within the combined framework of ModMax nonlinear electrodynamics and dRGT-like massive gravity. Operating in the extended phase space and employing the generalised Sharma-Mittal entropy to account for non-extensive statistical correlations, we derive exact analytical expressions for the modified Hawking temperature, specific heat, Joule-Thomson coefficient, and the equation of state. Our analysis of the throttling process reveals that the conformal nonlinearities of the ModMax field ($\gamma$) expand the physically accessible cooling domain by shifting the inversion transition to smaller horizon radii. While the Sharma-Mittal parameters ($\delta$, $R$) critically govern local thermodynamic stability and the inversion radius, the global inversion phase boundary remains fundamentally dictated by the massive graviton background. Furthermore, an analysis of the Gibbs free energy uncovers a van der Waals-like first-order phase transition characterized by a distinct swallow-tail structure. We observe a clear physical decoupling in the critical regime: ModMax nonlinearities modify the critical phase boundary by suppressing electromagnetic interactions, Sharma-Mittal parameters dictate the relative thermal stability of competing phases, and massive gravity governs the overarching macroscopic phase landscape. These results highlight the sensitivity of thermodynamic phase phenomena as robust diagnostic tools for distinguishing nonlinear and non-extensive modifications to black hole physics.

We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge $Q$. Using both a large-$N$ BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, $\chi\,\xi^{1/6}(24Q)^{1/9}\,\hbar\omega + \cdots$ where $\xi$ is the Bertsch parameter, and $\chi$ is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same $Q$ scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.

We present a field-level perturbative forward model for the Lyman-alpha (Lya) forest flux decrement. We validate it on two simulation suites: large-volume AbacusSummit N-body simulations with the Lya forest painted onto the dark matter field, and the Sherwood hydrodynamic simulations. Across the redshift range of the simulations (z=2.0-3.2), the 3D and 1D power spectra of the model match the simulated Lya fields at the 1% (5%) level up to k <= 0.3 (1.0) h/Mpc, with similar performance for the cross-correlation with massive dark matter halos. The counts-in-cells statistic shows excellent agreement down to cell radii of 2 Mpc/h. Leveraging cosmic variance cancellation, the model enables precision measurements of Lya bias parameters and robustly detects the full set of quadratic line-of-sight bias operators, consistent with the notion of naturalness in effective field theory (EFT). We quantify the stochasticity of the Lya forest (the analog to the one-halo term), and find it to be white (scale- and orientation-independent) on large scales, matching EFT predictions. We further find that phenomenological flux power spectrum models, based on modulations of the linear-theory power spectrum, fail at the field level even on quasi-linear scales. For the currently observing Dark Energy Spectroscopic Instrument (DESI), we generate large-scale clustering mocks of the Lya forest to validate cosmological parameter inference pipelines. Looking ahead to its successor, DESI-II, we produce large-volume mocks of representative samples of Lyman-break galaxies (LBGs) and Lya emitters (LAEs), calibrated on Astrid hydrodynamic simulations and matched to observations at z=3, enabling joint analyses of Lya forest and high-redshift galaxy data.

We develop a unified thermodynamic description of dynamic thin-shell wormholes, starting from the transparent (vacuum bulk) case and then relaxing the transparency condition to include bulk matter crossing the throat. For isolated shells, we show that the entropy is conserved under transparent evolution, $TdS=0$, which holds for arbitrary dynamical motion of the throat within the assumptions of the thin-shell formalism. When bulk matter is present, the generalised first law becomes $T\dot{S}=A\Phi$, where $\Phi$ is the net energy flux; entropy increases (decreases) when matter flows into (out of) the shell. Explicit expressions for the flux are provided for null dust and massless scalar fields, and quantum pair production (Hawking-like emission) is also discussed. A formulation of the generalised second law is presented, and it is consistent with standard thermodynamic expectations under conditions where heat flows from hotter to colder regions. As a concrete astrophysical application, we study accretion of null dust: the critical accretion rate above which the throat becomes dynamically unstable depends sensitively on the spacetime geometry and the shell equation of state, highlighting the environmental dependence of these configurations. Fluctuations in the energy flux induce a stochastic force on the throat dynamics, leading to a Langevin description with an associated fluctuation-dissipation relation. This results in diffusion of the throat radius and additional entropy production. The framework applies to a broad class of spherically symmetric thin-shell constructions within general relativity. Our results provide evidence that thin-shell wormholes admit a consistent thermodynamic description, quantify their sensitivity to accretion processes, and suggest possible avenues for probing exotic compact objects with future gravitational wave observations.

We investigate bipartite quantum correlations of Dirac fields in the spacetime of a Hayward regular black hole. Using the Wootters concurrence and the CHSH Bell parameter, we analyze the influence of Hawking radiation on an entangled state shared by an inertial observer and a near-horizon observer. We show that, unlike the bosonic case, fermionic correlations remain nonzero even in the infinite-temperature limit owing to the Pauli exclusion principle, while part of the entanglement is redistributed to inaccessible modes inside the horizon. The accessible modes exhibit Bell nonlocality for all finite Hawking temperatures, whereas the interior modes never violate Bell's inequality. The Hayward regularity parameter $g$ affects the correlations only through the Hawking temperature, whose decrease with increasing $g$ enhances the preservation of quantum information. These results suggest a close connection between singularity resolution and the robustness of fermionic quantum correlations in regular black-hole spacetimes.

The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to integrable Hamiltonians with local interactions involving multiple degrees of freedom. In this work we characterize both the continuous and discrete symmetries of these equations required to establish an equivalence class of solutions. We find that the set of such symmetries depend on the number of sites on which the equation is supported. In several cases there are more symmetries than the standard Yang-Baxter equation, thus placing heavy constraints on the number of inequivalent solutions and the associated integrable models.

Many phenomenological calculations involving massless or unstable particles suffer from divergences as mediating particles go on-shell. One way to deal with these divergences is via the Kinoshita-Lee-Nauenberg (KLN) theorem, which guarantees that by summing over all physically-degenerate processes, the divergences cancel and inclusive observables remain finite. However, actually implementing this theorem in practice requires handling disconnected diagrams, ill-defined distributional objects, threshold behavior and subtle regulator dependence. In this work, we formulate practical prescriptions for dealing with some of these issues by studying the KLN cancellation in an illustrative model exhibiting a t-channel divergence. We demonstrate intricate cancellations across several regularization schemes, connect our results to the complex-analytic structure of the underlying amplitudes, and take steps towards constructing a finite, fixed-order, inclusive t-channel collider observable. This work highlights both the utility of the KLN theorem, and also the technical subtleties and open questions involved with applying it in practice.

We show that there is an explicit resurgent duality between weak and strong coupling expansions when one of the expansions has zero radius of convergence and the other has infinite radius of convergence. This complements the situation where the convergent expansion has finite radius of convergence, or when both expansions have zero radius of convergence. We illustrate this phenomenon for the Airy and Pearcey catastrophe integrals, and we apply it to two physical examples: the weak and strong coupling expansions of Dyson-Schwinger equations in zero-dimensional scalar $\phi^4$ theories, and the short and long time expansions of the heat kernel trace for the fluctuation operator of the kink-antikink crystal saddle configuration in the Gross-Neveu model.

We present CHESS (CHEbyshev pSeudo Spectrum), a Wolfram Language package for high-precision one-dimensional transport of {\epsilon}-factorized differential equations for Feynman master integrals. The solver works with the matrix obtained by pulling a differential one-form to a chosen path. This matrix may be supplied directly, or assembled from constant matrices and precomputed scalar pullbacks of the one-forms. The program combines Chebyshev-Lobatto spectral collocation, sparse matrix assembly, sequential propagation in the {\epsilon}-expansion, and residue-based regularization of spurious regular singular endpoints. Benchmarks for large multi-scale integral families show rapid node convergence and agreement with independent reference data where such data are available. In the fixed local-series comparison used here, the Chebyshev transports also give shorter wall times; the reported process-tree memory usage is comparable for the smaller parallel runs and lower for the largest benchmark system in that comparison.

Under assumptions compatible with generic gravitational scattering, the vacuum relativistic gravitational field is entirely determined at leading order in the large radius expansion at spatial infinity by its supermomentum, its dual supermomentum and its global supertranslation frame. At subleading order, the gravitational field is determined by three additional sets of charges: the super-Lorentz charges, the leading tail charges and the leading peeling-breaking charges. In this work we provide a supertranslation-invariant definition of these charges in terms of asymptotic Bondi-Sachs fields as well as a corresponding supertranslation and logarithmic translation invariant definition of these charges in terms of Beig-Schmidt fields. Using the properties of homogeneous and inhomogeneous solutions to relevant wave equations over the boundary de Sitter spacetime at spatial infinity, we derive the conservation law of super-Lorentz charges between the future and past of spatial infinity. We obtain that the super-Lorentz aspects are non-locally defined from the Bondi-Sachs fields.

We use a primordial Majorana field as a fermionic probe of quantum correlations during inflation. Working in a torsion-free FLRW spacetime, we derive the two-component Majorana mode equations in an axion-inflation background and construct the corresponding quadratic Hamiltonian in the paired momentum basis. Hamiltonian diagonalization and the fermionic squeezing formalism are shown to give the same Bogoliubov transformation, providing a direct map from the Majorana mode functions to the instantaneous occupation number and to the two-mode state of each $(\boldsymbol{k},-\boldsymbol{k})$ pair. Because Fermi statistics restricts each helicity sector to the vacuum and one-pair states, the resulting Hilbert space is finite and the bipartite quantum-information measures can be evaluated explicitly. We compute the von Neumann entropy of the reduced mode and the logarithmic negativity of the Majorana pair. Both diagnostics indicate that sufficiently light Majorana modes can retain enhanced super-horizon bipartite quantumness, with the logarithmic negativity making the residual inseparability especially explicit. Our result does not by itself constitute an observational Bell test or a complete decoherence analysis; rather, it identifies a Pauli-bounded matter sector in which horizon exit alone is not sufficient to erase the quantum signature encoded in the two-mode state, thereby motivating an open-system study of how reheating and inflaton-induced interactions classicalize primordial fermionic probes.

We consider the sum of the adjoint Reidemeister torsions and prove the integrality for twist knots and the meridian. We also give some concrete examples of the generating functions for these sums.

The Hubble tension remains one of the most significant unresolved problems in modern cosmology. A key question is whether it may arise from underestimated systematic uncertainties in the different measurement techniques. In this context, new independent methods are of exceptional importance. We therefore pursue a novel approach to determining the Hubble constant, $H_{0}$ based on continuum time delay and spectral energy distribution (SED) modeling in active galactic nuclei (AGNs). Unlike conventional techniques, this method is entirely independent of the cosmic distance ladder and does not require cross-calibration against other distance indicators. As a result, it enables a direct determination of $H_{0}$, free from the arbitrary normalizations that often affect indirect measurements. We conducted a dedicated monitoring campaign of the Seyfert galaxy Fairall 9 and further developed the {\tt H0RIZON-AGN} model to interpret the resulting observations. The model incorporates the effects of radiation reprocessing in the surrounding cold accretion disk, enabling a more realistic description of the observed continuum delays. Through the simultaneous modeling of the continuum lag-spectrum and the broadband SED of Fairall 9, we derived a Hubble constant of $H_{0}=72.4_{-3.7}^{+3.4} \, \rm km \, s^{-1} \, Mpc^{-1}$. Achieving a measurement precision of approximately 5% from a single source demonstrates the considerable potential of this method for independent determinations of the Hubble constant. Our determination of $H_{0}$ is broadly consistent, within the current uncertainties, with both early- and late-Universe measurements. Future applications of the method to larger datasets, particularly those provided by the Vera Rubin Observatory, are expected to reduce the uncertainty to below 1%, thereby establishing this approach as a powerful independent probe of the Hubble tension.

We give an operadic approach to deformation quantization of vertex Poisson algebras, a chiral analogue of the traditional problem of deformation quantization of Poisson algebras. Our main result is an order-by-order deformation-obstruction theory for such quantizations, controlled by the chiral analogue of Poisson cohomology. In the special case of chiral quantizations of affine symplectic varieties, quantizations of the vertex Poisson algebras of functions on their arc spaces, we prove that this deformation-obstruction theory is controlled by their de Rham cohomology. As another application, we prove that the boundary Virasoro minimal models are rigid under deformations.

Investigating the non-perturbative behavior of QCD and the dynamics of strong interaction is crucial for the study of heavy quarkonia and the understanding of exotic fully-heavy tetraquarks. In this work, using the analytical exact iteration method (AEIM), the analytical eigenvalue solutions of the non-relativistic Schrödinger equation are obtained in the presence of topological defects and external magnetic flux. The interactions are modelled using a modified Cornell potential supplemented by harmonic and inverse quadratic terms. We demonstrate that the energy levels are distinctly shifted by the topological defect parameter ($\alpha$). The mass spectra of heavy quarkonia ($c\bar{c}$ and $b\bar{b}$) and fully-heavy tetraquarks ($cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$) across several radial and orbital excitation states are successfully calculated using this approach. The computed masses of bottomonium and charmonium accord well with current theoretical predictions and experimental findings. Our findings for the heavy tetraquarks are in line with previous theoretical investigations that consider tetraquarks as configurations of diquarks and antidiquarks. The numerical results demonstrate that a nontrivial interaction between the confining potential and the background space-time geometry governs the mass hierarchy of these exotic hadronic states, providing high-precision data with excellent agreement with established theoretical models and experimental benchmarks.

I propose a Hermitian extension of the Lorentz-symmetric Dirac theory by complementing the associated Hamiltonian with another \emph{masslike} anticommuting Dirac operator. The resulting theory manifests the iconic linear energy-momentum relationship in any dimension ($d$) and hence the emergent nodal quasiparticle excitations are named \emph{hidden-ordered Dirac fermions}, which are symmetry protected and their responses are analogous to those in original Dirac systems, however, in terms of a renormalized (due to the hidden ordering) Fermi velocity. Typically, such a hidden ordering pushes any quantum phase transition into an insulation toward even stronger coupling in any $d>1$. However, depending on the internal algebra between the candidate insulating order parameter and masslike Dirac operator, the hidden-ordering may survive or disappear near the corresponding itinerant quantum critical point. I construct lattice models for such hidden-ordered massless Dirac fermions and outline promising platforms (numerical and experimental) to test these predictions.

In a Lorentz symmetric non-Hermitian (NH) Dirac theory, containing the canonical relativistic Hamiltonian accompanied by a masslike anti-Hermitian Dirac operator, when the associated NH parameter becomes spatially modulated it couples massless Dirac fermions as NH gauge fields. With specific choices of such resulting NH gauge potential, the system experiences NH magnetic fields. When a planar Dirac system encloses a finite flux of such NH magnetic fields, a manifold of spatially localized \emph{right or left} zero-energy eigenmodes appear in the spectrum, which we numerically anchor from microscopic realizations of NH magnetic fields on graphene's honeycomb lattice. Potential experimental platforms to test these predictions are discussed. Altogether, zero-energy NH flat bands of right or left modes promise fascinating future realizations of NH magnetic catalysis, strongly-coupled NH fractional topological phases, and NH chiral anomaly, to name a few.

By extending the new supersymmetric localization principle introduced in \cite{Choi:2021yuz}, we present a path integral derivation of the Selberg trace formula on arbitrary compact Riemann surfaces, including the case of vector-valued automorphic forms of arbitrary half-integer weight corresponding to Maass Laplacian. We also generalize the method to formulate the Selberg trace formula on generic compact locally symmetric space.

This work is a continuation of the program initiated in [arXiv:2311.18302]. We show how one can define novel gauge-theoretic (holomorphic) Floer homologies of seven, six, and five-manifolds, from the physics of a topologically-twisted 8d $\mathcal{N}=1$ gauge theory on a Spin$(7)$-manifold via its supersymmetric quantum mechanics interpretation. They are associated with $G_2$ instanton, Donaldson-Thomas, and Haydys-Witten configurations on the seven, six, and five-manifolds, respectively. We also show how one can define hyperkähler Floer homologies specified by hypercontact three-manifolds, and symplectic Floer homologies of instanton moduli spaces. In turn, this will allow us to derive Atiyah-Floer type dualities between the various gauge-theoretic Floer homologies and symplectic intersection Floer homologies of instanton moduli spaces. Via a 2d gauged Landau-Ginzburg model interpretation of the 8d theory, one can derive novel Fukaya-Seidel type $A_\infty$-categories that categorify Donaldson-Thomas, Haydys-Witten, and Vafa-Witten configurations on six, five, and four-manifolds, respectively -- thereby categorifying the aforementioned Floer homologies of six and five-manifolds, and the Floer homology of four-manifolds from [arXiv:2311.18302] -- where an Atiyah-Floer type correspondence for the Donaldson-Thomas case can be established. Last but not least, topological invariance of the theory suggests a relation amongst these Floer homologies and Fukaya-Seidel type $A_\infty$-categories for certain Spin$(7)$-manifolds. Our work therefore furnishes purely physical proofs and generalizations of the conjectures by Donaldson-Thomas [2], Donaldson-Segal [3], Cherkis [4], Hohloch-Noetzel-Salamon [5], Salamon [6], Haydys [7], and Bousseau [8], and more.

By applying the new supersymmetric localization principle introduced in \cite{Choi:2021yuz,Choi:2023pjn}, we present two complementary approaches for the path integral derivation of the `non-chiral' trace formula for a semisimple compact Lie group $G$, which generalizes the so-called Frenkel trace formula. Corresponding physical systems for each picture are the quantum mechanical sigma model on $G$ and the gauged sigma model on $G\times G$, and the approaches closely follow the spirit of the Eskin trace formula \cite{Choi:2021yuz} and the Selberg trace formula \cite{Choi:2023pjn} respectively. These methods provide a natural conceptual bridge between two seemingly independent derivations in \cite{Choi:2021yuz} and \cite{Choi:2023pjn}.

A supersymmetric version of the Virasoro minimal string was defined some time ago using random matrix model techniques. Several of the special properties of the matrix model that were noted (accessible fully non-perturbatively) underlie features shared by both 0A and 0B versions of the theory. This paper develops the formalism much further, including showing how the 0A and 0B choices familiar in continuum approaches have a direct analogue in terms of building solutions of the appropriate string equations. This also illuminates several key differences between the 0A and 0B models at the level of matrix model loop observables. The natural all-orders vanishing of loops, already observed in some 0A models, translates into the same for 0B. It is also noted that the leading amplitude for a single asymptotic boundary, as well as the trumpet partition function, are characters of a 2D superconformal field theory living on the boundary of a solid torus, suggesting a 3D chiral supergravity dual. Non-perturbative results are computed as well.

The chiral SYK model is a 1+1 dimensional generalisation of the Sachdev-Ye-Kitaev model with chiral Majorana fermions and homogeneous random interactions. In the large-N limit, the model admits an exact solution of the two-point function due to its scaling symmetry and exhibits a quantised thermal Hall conductance consistent with that of a 2+1-dimensional gapped topological system. We study two chiral SYK systems coupled by a relevant quadratic interaction that explicitly breaks scaling and time-reversal symmetry. Working in the regime of weak intersystem coupling, we solve the Dyson-Schwinger equations perturbatively and obtain analytic expressions for two-point functions at finite temperature. Unlike the coupled SYK model in 0+1 dimensions, the 1+1-dimensional chiral system does not develop a mass gap, and no thermal phase transition is observed. We show that the leading correction to the thermodynamic free energy is temperature independent, implying that the entropy density remains identical to that of two uncoupled chiral SYK systems. A real-time analysis of the retarded correlator reveals the emergence of massless collective bosonic modes propagating between the two subsystems at zero temperature, signalling quasiparticle tunnelling without gap generation. Our results demonstrate a sharp qualitative distinction between relevant deformations of SYK models in zero and one spatial dimensions, and highlight the robustness of gapless chiral edge dynamics against explicit scaling symmetry-breaking interactions.

In the presence of 't Hooft anomalies, backgrounds for the symmetries of a quantum field theory can lead to non-conservation of Noether currents, or more generally, to the presence of charged insertions in the path integral. When there is a net background charge, the partition function evaluated on closed manifolds will vanish. For anomalous symmetries, this statement can also be understood as the anomaly theory giving rise to a non-trivial anomalous phase for the partition function even for "rigid" transformations which leave all background fields unchanged. We use the generalisation of this second viewpoint to the setting of anomalous higher-form symmetries in order to show vanishing of the partition function for a number of examples, both with and without a Lagrangian description. In particular, we show how to derive from these considerations the analogue of the Freed-Witten anomaly cancellation condition for the M5-brane, and also that for the D3-brane in S-fold backgrounds.

Over the last few decades, a rich structure has been uncovered in the infrared sector of various field theories. This mostly comes through the connections between memory effects, asymptotic symmetries, and soft theorems (the ``infrared triangle''), which have been explored in much depth within high-energy physics. In this paper, we show how sound also admits an infrared triangle. We consider the linear perturbations of the Euler equations for a barotropic and irrotational fluid. We then show how low-frequency changes in an acoustic source can lead to lasting displacements of fluid particles. We proceed to write these linear perturbations in terms of a two-form potential -- a Kalb--Ramond field, in the high-energy physics terminology. This phrases linear sound as a gauge theory. Standard techniques can then be used to probe the infrared structure of acoustics. We show how the memory effect relates to asymptotic symmetries in this dual formulation, and comment on how these notions can be connected to soft theorems. This exhibits an example of an infrared triangle in a condensed matter system and provides new pathways to the experimental detection of memory effects.

We introduce the orthogonal Grassmannian as a novel kinematic space for describing correlators of massless spinning fields in de Sitter space. By automatically encoding the constraints of conformal symmetry and current conservation, the formalism drastically simplifies these correlators. We show that three-point functions are fixed by little group covariance and take the same form as the corresponding Schwinger-parameterized correlators in twistor space. The power of the Grassmannian approach is especially evident for four-point functions, which require dynamical input beyond kinematics. We demonstrate that unitarity enforces the same factorization properties as for scattering amplitudes and use these to bootstrap the four-point functions in several non-trivial examples, including Yang-Mills theory and gravity. We find expressions that are astonishingly simple and reveal a close connection to the corresponding scattering amplitudes. Our results suggest that the Grassmannian provides the natural language for spinning correlators in de Sitter space and illuminates their geometric origin.

Homogeneous and isotropic equilibrium states of strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills charged plasma in ${\mathbb R}^3$ with equal chemical potentials for the maximal Abelian subgroup of the $R$-symmetry group become dynamically unstable below some critical temperature. The instabilities arise in the $R$-symmetry charge transport, precisely when the equilibrium state becomes thermodynamically unstable. We study the fate these correlated instabilities when the theory is placed on $S^3$. The curvature of the three-sphere affects the onset of the dynamical and the thermodynamic instabilities differently: increasing the curvature at low temperatures can stabilize its transport, but leave the plasma thermodynamically unstable. Thermodynamic stability is never recovered provided the $S^3$ volume is allowed to fluctuate.

We establish a correspondence between vortex equations on flat Riemann surfaces and harmonic spinors on the Nappi--Witten space, the group manifold of a central extension of the Euclidean group $SE(2)$. Vortex configurations lift naturally to this setting, producing explicit solutions of a twisted Dirac equation. Using the conformal flatness of the Nappi--Witten metric, these solutions induce harmonic spinors on four-dimensional Minkowski space. This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data.

We study zero-temperature false vacuum decay in $D$ compact spatial dimensions and show that for volumes below a critical value a new bounce solution, different from Coleman's celebrated $O(D)$ bubble, mediates the decay process, and typically leads to an exponentially enhanced decay rate. The bounce, when analytically continued to Lorentzian signature, nucleates a homogeneous field configuration for spatial volumes below a critical value, and quasi-homogeneous configurations for slightly larger volumes, and is not of the form of a thin or thick-walled bubble embedded in a false vacuum background. We explicitly show that the new bounce has the necessary features associated with false vacuum decay, following from its eigenvalue spectrum of fluctuations. The cross-over from homogeneous to quasi-homogeneous solutions as the spatial volume is increased is discussed, as is a real-time interpretation of the bounce. We apply this bounce to the study of a scalar field model, as well as a close cousin of the Schwinger effect that applies to $(1+1)d$ axion electrodynamics in compact space.

We study the gauge-invariant dynamically conserved charges, and their corresponding densities, for instanton solutions of Yang-Mills theories in four dimensional Euclidean space, for the gauge group $SU(2)$. Those charges were constructed in [1,2] through the integral equations of Yang-Mills theory, using techniques on generalized loop spaces. We use the integral non-Abelian Gauss law to evaluate the gauge-invariant flux of the magnetic and electric non-Abelian fields through spherical surfaces centered at the origin of the instanton solution. From such a flux, we define gauge-invariant charge densities by considering the charge within an infinitesimal spherical shell of radius $r\equiv\sqrt{x_i \, x^i}/\lambda$, with $\lambda$ being the parameter of the instanton solution, defining its size, and $x_i \, x^i = (x^1)^2 + (x^{2})^2 + (x^{3})^2$. We discuss the issue of the reparameterization invariance of the charges and densities, and show that the magnetic and electric fluxes for the instanton and anti-instanton, at $r=1$ and $x^4 = 0$, $x^4$ being the Euclidean time, are non-zero and observable. Our results give an interesting picture of the internal structure of the instanton, and may be important for the properties of the Yang-Mills $\theta$-vacuum.

We show that the moment of the transfer matrix of the double scaled SYK model is written as an overlap between the stationary state of ASEP (asymmetric simple exclusion process) and a product state. We argue that this overlap is an analogue of the strange correlator appearing in the correspondence between the Levin-Wen string-net model and the Turaev-Viro state sum.

A variational principle for quantum-state distinguishability is established in many-body systems with generalized symmetries, including noninvertible cases described by fusion categories. Standard fidelity and symmetry-resolved diagnostics emerge as coarse-grained limits of a more refined operational structure. When symmetry actions terminate at entanglement cuts, distinguishability is governed by boundary tube algebras within a symmetry-constrained measurement resource theory. The physically admissible instruments are characterized by complete positivity, entanglement-cut locality, boundary-module covariance, and sequential stability. The resulting optimal measurement structure is uniquely fixed by the center of the boundary tube algebra, $\mathcal{A}_{\mathrm{phys}} = Z\!\left(\mathrm{Tube}_{\mathcal{C}}(\mathcal{M}_A)\right)$, whose primitive dempotents define tube-sector probabilities that refine fidelity-based and symmetry-resolved descriptions. The associated tube positive-operator-valued measures (POVMs) are extremal and yield optimal one-shot hypothesis-testing distinguishability under symmetry constraints. The categorical selection rule is universal across fusion categories and independent of microscopic realization; microscopic models enter by choosing the boundary module and the protocol family used to witness a nontrivial tube fiber.

We construct magnetic and electric Carrollian Maxwell theories by performing Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background with manifest gauge symmetry. The procedure preserves a first-class U(1) Gauss constraint throughout the Carrollian limit. Gauge invariance is therefore maintained in our Hamiltonian formulation. By choosing different scalings, we obtain standard magnetic Carrollian theory and electric Carrollian theory. However, a scalar field could appear in the Carrollian theory in a coupled or decoupled way, which has not been found by previous methods. This result fully reveals the diversity of Carrollian theories accessible through the deformed light-cone Kaluza-Klein-like null reduction method. Furthermore, our work provides an explicit example of the correct application of this approach, thereby broadening the scope of its applicability to gauge theories.

In this paper, using connected compact oriented smooth 4-manifolds, some representations of the hyperfinite II_1-type factor von Neumann algebra are constructed. The Murray--von Neumann coupling constant of these representations gives rise to a new smooth 4-manifold invariant whose very first properties are investigated. Moreover as a part of this construction, a connected compact oriented smooth 4-manifold admits an embedding into the hyperfinite II_1 factor. This embedding, on the one hand, induces a Riemannian metric on the manifold such that its Riemannian curvature tensor belongs to the von Neumann algebra; on the other hand the metric induces a periodic dynamics on the von Neumann algebra, what we call the Hodge dynamics on the hyperfinite II_1 factor. It is observed that the metric is Einstein i.e., satisfies the (Riemannian) vacuum Einstein equation with a possibly non-zero cosmological constant, if and only if its Riemannian curvature tensor belongs to the fixed-point-subalgebra of the Hodge dynamics. Finally, we make a comprehensive enumeration of all representations of the hyperfinite II_1 factor constructed here, from the viewpoint of thermal equilibrium states and phase transitions in algebraic quantum field theory.

Quantum systems invariant under particle exchange are either Bosons or Fermions, even though quantum theory in principle admits more general behavior under permutations. But why do we not observe such paraparticles in nature? The analysis of this question was previously limited primarily to specific quantum field theory models. Here we give two distinct model-independent arguments that rule out parastatistics, i.e. fundamentally indistinguishable quantum systems transforming under higher-dimensional representations of the symmetric group, which draw on quantum information theory and recent research on internal quantum reference frames. First, we introduce a notion of complete invariance: quantum systems should not only preserve their local state under permutations, but also the quantum information they carry about other systems, in analogy to the notion of complete positivity in quantum information theory. Second, we demand that quantum systems are invariant under quantum permutations, i.e. permutations conditioned on values of permutation-invariant observables. For both, we show that the respective principle is fulfilled if and only if the particle is a Boson or Fermion. Our results show how quantum reference frames can shed light on a longstanding problem of quantum physics, they underline the crucial role played by the compositional structure of quantum information, and demonstrate the explanatory power but also subtle limitations of recently proposed quantum covariance principles.

The average subsystem trace distance has been proposed as an indicator of quantum many-body chaos and integrability. However, evaluating it presents two main difficulties: high computational cost for large systems and ambiguities in defining and ordering eigenstates in integrable systems. In this work, we develop an efficient algorithm to compute the Bures distance between fermionic Gaussian states, enabling access to larger system sizes. Using this method, we calculate the average subsystem Bures distance for eigenstates in the spin-1/2 transverse-field Ising chain and the Dirac fermion formulation of the quadratic Sachdev-Ye-Kitaev (Dirac SYK$_2$) model, as well as for random pure fermionic Gaussian states. To handle degeneracy in the Ising chain, we consider simultaneous eigenstates of all local conserved charges and employ these charges to systematically order degenerate states. Our results are consistent with the earlier conjecture of a linear growth with subsystem size. We show that the distinct scaling of the average subsystem distances in chaotic versus integrable systems originates from discontinuities of local conserved charges across the spectrum in integrable models. For the Dirac SYK$_2$ model and random pure Gaussian states, we obtain similar results for the average subsystem distances, which do not show a linear increase.

It is well known that the noninteracting Majorana chain is dual to the one-dimensional transverse-field Ising model, either through the Jordan-Wigner transformation or by gauging fermion parity. In this correspondence, the minimal translation of the Majorana chain maps to the celebrated Kramers-Wannier (KW) duality of the spin model, with the critical point mapped to the self-dual point. In this work, we generalize this mapping to two and higher dimensions by constructing a unitary equivalence between the parity-gauged fermionic system and a spin system defined on arbitrary polyhedral decompositions of space. Imposing the flatness condition on the gauge field yields a bosonization duality between the original (ungauged) fermionic system and a gauged spin system obeying a Gauss law. The dependence of the Gauss law in the spin system on the Kasteleyn orientation (and the discrete spin structure) of the fermionic system is made explicit. Applying this bosonization to one or two copies of Majorana fermions on translationally invariant lattices, we derive higher-dimensional analogs of KW (self-)dualities in spin systems arising from fermionic minimal translations. The KW (self-)dualities are non-invertible due to projections onto eigenspaces of higher-form symmetries in the associated symmetry operators. The bosonization framework we present is intuitive, general, and systematic, encompassing other known exact bosonization methods while offering a novel approach to establish new connections between fermionic and spin systems in arbitrary dimensions.

Aoki, Fukaya, and Taniguchi claim that both the spectral density of the Dirac operator at the origin and the topological susceptibility must vanish identically for sufficiently small but nonzero quark mass $m$ in the chirally symmetric phase of quantum chromodynamics with two light quark flavors, under certain technical assumptions on the spectrum and on the dependence of observables on $m$. I argue that a crucial step of their proof is not justified, and the validity of these conclusions should be reassessed.

Integrable trotterization} provides a method to evolve a continuous time integrable many-body system in discrete time, such that it retains its conserved quantities. Here we explicitly show that the first order trotterization of the critical {\it transverse field Ising model} is integrable. The discrete time conserved quantities are obtained from an inhomogeneous transfer matrix constructed using the {\it quantum inverse scattering method}. The inhomogeneity parameter determines the discrete time step. We then focus on the non-invertible {\it Kramers-Wannier} duality-symmetry for the trotterized evolution. We find that the discretization of both space and time leads to a doubling of these duality operators. They account for discrete translations in both space and time. As an interesting application, we find that these operators also provide maps between trotterizations of different orders. This helps us extend our results beyond the trotterization scheme and investigate the Kramers-Wannier duality-symmetry for finite time Floquet evolution of the critical transverse field Ising chain. {Finally, we investigate how these non-invertible operators shape the phase diagram of the discrete-time evolution. This question is particularly interesting in the Floquet setting, which is known to host a richer phase structure than its undriven counterpart. We systematically construct the necessary operators which relate different phases away from criticality for both trotterized and Floquet evolutions.

We study the impact of combining the present NO$\nu$A and T2K data with simulated data from the JUNO experiment on the determination of the leptonic CP phase and the neutrino mass hierarchy. The current NO$\nu$A data exhibit a hierarchy--$\delta_{\rm CP}$ degeneracy, admitting both normal hierarchy (NH) with $\delta_{\rm CP} \in [0,180^\circ]$, and inverted hierarchy (IH) with $\delta_{\rm CP} \in [180^\circ,360^\circ]$ solutions at comparable significance, while T2K prefers $\delta_{\rm CP}\simeq 270^\circ$ for both hierarchies, leading to a $2\sigma$ tension between the two experiments for normal hierarchy. Using detailed GLoBES simulations, we show that future JUNO data with excellent hierarchy sensitivity, can lift the hierarchy--$\delta_{\rm CP}$ degeneracy in NO$\nu$A and strengthen the hierarchy reach of T2K in spite of having no $\delta_{\rm CP}$ sensitivity. Allowing the hierarchy to be a free parameter in the fit, if the true ordering is IH, JUNO aligns the NO$\nu$A and T2K allowed regions and resolves their present tension; if NH is true, the tension continues to persist. We also show that JUNO's precise measurement of $|\Delta_{31}|$ leads to improved constraints on $\sin^2\theta_{23}$ and $\delta_{\rm CP}$ for normal mass hierarchy in NO$\nu$A even though JUNO itself is insensitive to these parameters. Finally, updated solar parameter measurements from JUNO's first data release further enhance the combined precision. Our results demonstrate that JUNO plays a crucial synergistic role in the global neutrino oscillation programme, enabling a more robust determination of the mass ordering and improving the sensitivity to the CP phase when combined with long-baseline data.

We develop an effective field theory framework for the conservative linear tidal response of a relativistic neutron star modeled as a perfect fluid with conserved particle number. Starting from the covariant fluid action in a curved background, we linearize about a static equilibrium configuration and obtain the quadratic action for fluid displacements coupled to metric perturbations. We then split the metric perturbation into induced and externally sourced parts, and integrate out the induced metric on a conservative matched domain using a symmetric Green kernel. The resulting effective fluid theory contains metric-mediated fluid interactions through a self-adjoint operator acting on the displacement, while the external perturbation acts as a tidal source. This self-adjoint structure permits a modal expansion of the pole sector: after projection onto conservative eigenmodes, the dynamics reduce to tidally driven oscillators with couplings fixed by relativistic inner products and overlap integrals. Matching these oscillator variables to the quadrupolar worldline theory gives analytic expressions for the modal dynamical tidal deformabilities in terms of mode frequencies, normalizations, and overlap integrals. We also identify a source-only non-pole sector generated by terms quadratic in the external perturbation. This sector does not affect the mode amplitudes, but its electric-quadrupolar projection can contribute to the full tidal response. This formulation clarifies which part of the relativistic tidal response is captured by explicit fluid modes and where a possible source-only non-pole contribution enters the worldline description.

The renormalized scalar mass squared is a function of the energy scale and power-runs as its square. Well above the electroweak scale, its dimensionless couplings evolve only slowly, so the Standard Model is approximately scale invariant, and an order-one boundary value supplied at the unification scale is mapped exponentially down to the electroweak scale, much as the QCD scale arises from a dimensionless coupling alone. The 28 orders of magnitude separating the two then measure the smallness of an anomalous dimension, dominated by the top-quark Yukawa coupling, rather than a tuning. Naturalness is thereby recast as the value of an order-one ratio, with no protective symmetry required.

While the positive Grassmannian is deeply understood through the rich combinatorics of plabic graphs and positroid cells, its tropical counterpart, the positive tropical Grassmannian Trop$_{>0}G(k,n)$, has lacked a comparable structural framework for general $k$. Both the global face structure of Trop$_{>0}G(k,n)$ and the internal metric geometry of the tropical linear spaces it parametrizes have remained largely uncharted. This paper develops a systematic algebraic and polyhedral foundation that resolves this gap. The engine of our framework is a fundamental tropical duality, analogous to the duality between cluster variables (or more precisely, their $u$-coordinates) and $\mathbf{g}$-vectors, pairing two families of objects introduced by the first author: the planar basis of tropical Plücker vectors and the planar cross-ratios on the positive configuration space. We prove that this duality links the fan structure of the positive tropical Grassmannian to the noncrossing fan of Santos, Stump, and Welker, yielding a global bijection between integer points of $Trop_{>0}G(k,n)$ and noncrossing tableaux. We then study how this discrete combinatorial data controls the continuous metric geometry of positive tropical linear spaces. We realize the bounded complex of an integer positive tropical linear space as the subdifferential of a central roof function on the hypersimplex, and use this realization to embed it into a dilate of the fundamental alcoved simplex. The dilation factor, and hence the geometric diameter of the complex, is governed by a single invariant, the planar kinematics ($K) weight, which we show equals the number of columns in the associated noncrossing tableau. The results of this work are applied in our parallel work on scaffolds for higher tropical Grassmannians.

We compare Picard--Lefschetz theory and resurgence in three basic one-dimensional exponential integrals: the Airy model, the Bessel model, and the Gamma model. On the Picard--Lefschetz side, we describe the Lefschetz thimbles and compute the connecting trajectories between critical points appearing at Stokes phases. On the resurgent side, we analyze the Borel singularities of the saddle expansions and use alien operators to recover the same Stokes coefficients. These examples serve as explicit finite-dimensional test cases for the dictionary between thimble wall-crossing and alien calculus.

A key challenge of gravitational-wave physics is distinguishing the nature of compact objects involved in binary coalescences, particularly whether they are black holes or neutron stars. Neutron stars are distinguished from black holes by a stronger tidal response, with both static and dynamical aspects directly linked to their rich internal physics. Measurements of the tidal response through gravitational observations constrains the neutron-star equation of state and provides insight into the physics of high-density matter. However, defining the tidal response of neutron stars in general relativity is challenging due to coordinate ambiguities and the complexity of connecting the star's response to binary dynamics and the associated gravitational waveforms. In this paper, we show how the dynamical tidal response of a neutron star can be systematically defined within the worldline effective field theory (EFT) framework, connecting the problem to gravitational-wave scattering off an isolated neutron star. These scattering amplitudes are computed both within the EFT, using standard quantum field-theory techniques, and within stellar perturbation theory (the corresponding ultraviolet theory), where the coupled metric and matter perturbation equations are solved in the stellar interior within general relativity and matched to the analytical Mano-Suzuki-Takasugi (MST) solutions in the exterior. We match the scattering amplitude between effective theory and the ultraviolet theory to obtain the dynamical tidal response. We show the result to be consistent with known expectations, such as the static limit and the behaviour near the neutron star's resonant modes, while also recovering the imaginary part of the dominant oscillation mode induced by gravitational-wave dissipation. We conclude with a discussion of potential future improvements within both the EFT and the perturbation theory.

We classify 4-dimensional gravitational theories with integrability properties analogous to quasi-topological gravity, but for metrics with the symmetries of spherical, hyperbolic, and planar Schwarzschild and Taub-NUT solutions, their double-Wick-rotated counterparts - the B-metrics, the near-horizon extreme Kerr, and the swirling universe - and the Eguchi-Hanson instanton. These are the symmetries that allow consistent reductions (principle of symmetric criticality) with 4 Killing vectors and 3-dimensional orbits. Considering theories depending only on the Riemann tensor, we show that, for these metrics, only those with third-order equations (second-order after trivial integration) can be analytic in the Riemann tensor. We show that there is a unique theory with first-order field equations (algebraic after trivial integration, with the same integrability as general relativity) at each order in curvature and construct regular static black holes from infinite towers of these high-energy corrections to general relativity. For these theories, we obtain closed-form solutions for all the symmetries listed above, which we analyze to ensure they have a clear physical interpretation.