Papers

Can a holographic theory be reconstructed from its equation of state? We investigate this question using physics-informed neural networks in the bosonic-mass sector of the Pilch–Warner model. We first validate the PINN approach against an analytic solution encoding the leading high-temperature corrections to the conformal equation of state. We then reconstruct nonlinear black-brane geometries and the scalar potential using thermodynamics, ultraviolet asymptotics, Ward identities, and horizon regularity. Independent solutions of the bulk Einstein-scalar equations demonstrate that accurately reproducing thermodynamics with a trained PINN does not guarantee an accurate reconstruction of the scalar potential. High-precision knowledge of the high-temperature equation of state constrains nonlinear interactions in the bulk scalar potential. Fixing the cubic coupling to its exact PW value, motivated by this high-temperature extraction, reduces the maximum sampled error in the reconstructed scalar self-interactions by a factor of $\sim 15$ compared with constraining only the bulk scalar mass. Adding knowledge of the bulk viscosity of the gauge theory plasma further reduces this error by an additional factor of $\sim 13$, with independent forward solutions reproducing the bulk viscosity within $0.09\%$.

We construct a chiral algebra $U$ of central charge eight inside the lattice vertex operator algebra $V_{E_6\oplus A_2}$. It is generated by two commuting affine $\mathfrak{sl}_2$ current algebras at levels $1$ and $39$, the stress tensor of the lattice theory, and a single weight-two field built from three lattice exponentials. We announce that $U$ is strongly rational and completely unitary, and that $Rep(U)$ is equivalent, as a unitary ribbon category, to the Drinfeld center $Z(\mathcal{H}_3)$ of the Haagerup fusion category $\mathcal{H}_3$. Its characters are the $\gamma=0$ Evans–Gannon vector. From $U$ we obtain a diagonal full CFT, and also a holomorphic $E_8$ extension on which $\mathcal{H}_3$ acts by topological defects.

Characteristic modes provide important information about the intrinsic properties and dynamical response of gravitational systems. In this work, we investigate characteristic modes of thick branes with a non-minimally coupled bulk scalar field. Two representative thick brane solutions are considered, corresponding to a single-kink scalar configuration and a deformed kink configuration with internal structure, respectively. By analyzing the tensor perturbation equations, we first examine the localization of the graviton zero mode in the two brane models. For both brane models, the graviton zero mode is localized on the brane. No pronounced resonant Kaluza–Klein (KK) modes are found for the single-kink brane at $\xi=1/7$. For the deformed brane, we investigate the resonant KK modes at $\xi=0.99$, finding that increasing the deformation parameter $k$ leads to more resonant modes and a longer-lived first resonance. We then calculate the quasinormal modes (QNMs) of both brane models independently in the frequency and time domains. The quasinormal frequencies (QNFs) obtained by the independent methods agree well for the low overtones. The masses and decay rates of the resonant KK modes agree closely with the real parts and the magnitudes of the imaginary parts of the corresponding QNFs, respectively.

We present a suite of 50 unpublished research-level theoretical physics problems with verifiable answers. Without AI assistance, a typical problem in our collection could be solved by a world expert in about a day or less but would take considerably longer for experts in adjacent specialties. We test the ability of off-the-shelf AI agents to tackle these problems autonomously, without human hints. When given access to tools available in a realistic setting, including the ability to search the literature and write scripts for numerical and symbolic work, the best-performing agent, GPT-6-Astra harnessed in Codex, obtains the final answers with a near-perfect accuracy of 98% at an average cost under USD 3 per problem. On average, agents show only small changes in accuracy when denied web search and access to background research papers, suggesting significant memorization of the literature. These results suggest that state-of-the-art agents can accurately perform concrete calculations required across theoretical physics research. We comment on the broader implications of these findings and discuss possible explanations for the current lack of agent-led breakthroughs in theoretical physics despite their outstanding problem-solving abilities.

We investigate non-stationary wormhole geometries in General Relativity embedded in evolving cosmological backgrounds. We employ a Simpson-Visser-like regularization of the temporal coordinate of the $(n+1)$-dimensional FLRW metric, together with a homogeneous Cuscuton field, to construct cosmological backgrounds in which the scale factor remains finite and non-zero at the would-be initial singularity. We then consider two specific dynamical wormhole geometries: the four-dimensional defect wormhole and the topologically charged Perry-Mann type wormhole. We show that the former can be supported by a canonical scalar field with vanishing potential, while the latter requires a mimetic matter sector to support its spatial structure, with the Cuscuton governing the cosmological evolution in both cases. We subsequently generalize the analysis to a separable non-stationary spacetime and derive a scaling condition that strongly constrains the admissible matter sources. In particular, for minimally coupled scalar and nonlinear electrodynamics fields, this condition removes the functional freedom available in static reconstruction schemes. We show that, within this framework, regular, asymptotically flat wormhole geometries cannot be obtained while simultaneously satisfying the required smoothness and reflection symmetry conditions. Our results illustrate both the possibility of constructing specific non-stationary wormholes in regular cosmological backgrounds and the restrictions that arise when attempting to generalize such constructions to arbitrary spatial geometries.

We develop a framework for computing the nonlocal one-loop effective action in scalar and spinor QED at finite temperature and chemical potential in arbitrary even spacetime dimensions. Based on the heat kernel expansion to quadratic order in background fields, the framework reduces the effective action form factors to a common fundamental kernel. By resumming the external-momentum expansion, we obtain explicit closed-form expressions for the massless form factors in terms of polylogarithms and their derivatives with respect to the order. The same method determines the coefficients of the small-mass expansion to arbitrary order. The resulting expressions retain the full dependence on external Euclidean momentum, temperature, and chemical potential, without invoking the soft-momentum approximation. We also derive the corresponding photon polarization operators and evaluate their static limits, obtaining the Debye screening masses and electromagnetic susceptibilities.

We study supersymmetric vacua of three-dimensional $\mathcal N=1$ effective theories from type IIA, type IIB/type I, and heterotic compactifications on $G_2$-structure spaces. Superpotential homogeneity and the physical scalar metric yield universal vacuum relations and axion stabilization constraints without specifying the full moduli-space metric. We express AdS$_3$ scalar masses through $\Delta$, the scaling dimension of the corresponding operator in the dual two-dimensional conformal field theory. In massive type IIA AdS$_3$ vacua, we derive the bound $\Delta_{\max}\geq(20+4\sqrt{67})/7\approx 7.5$ and an exact dimension $\Delta_b=6$ for $B_2$ axions on the torsion-free branch. Type IIB type I and heterotic AdS$_3$ vacua contain a universal volume-dilaton mode with $\Delta_{\phi s}=4$. On the singlet-torsion type IIB branch, we also obtain the volume-dilaton mode with $\Delta_{\phi s}=20/7$ and $\Delta_b=16/7$. Every supersymmetric Minkowski vacuum in the retained classical closed-string theories possesses an exact volume-dilaton flat direction. We characterize physical large-flux limits after tadpole constraints and axionic identifications, and identify torsion obstructions to isotropic scale separation.

Here we perform a Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions of a partially broken Fronsdal model for spin-3 and spin-4. The reduced models describe massive spin-3 and spin-4 particles without extra propagating modes. They differ from Singh-Hagen models by quadratic terms which vanish on shell, similarly to their higher dimensional massless parents. A covariant description of the reduced models in terms of gauge invariant field combinations naturally leads to higher derivative models, contrary to lower spin cases ($s\le 2$). For both $s=3$ and $s=4$ we have a rather peculiar massless limit. Although their particle content corresponds to the $\pm j$ helicities with $j=0,1, \cdots s$, as expected, they appear intertwined in a non trivial way preventing diagonalization through any local field redefinition.

We construct an algebraic framework for the extended holomorphic anomaly equations following ideas of Alim, Movasati, Scheidegger and Yau. We choose the quintic threefold as our main model and use this framework to solve the equations and fix the ambiguity up to genus 5. We obtain predictions for real Gromov-Witten invariants, or, equivalently, real Gopakumar-Vafa invariants that are integers and agree with their complex counterparts modulo 2. In the end, we discuss how the framework could be extended and compute the same predictions for the bicubic up to genus 9.

The $248$ keV nuclear-recoil candidate reported by LUX-ZEPLIN (LZ) motivates an inelastic dark matter (DM) interpretation, in which scattering converts the DM particle into a slightly heavier state. We provide a comprehensive study of this interpretation in an anomaly-free model of gauged baryon number, where a new vector boson, $Z_B$, mediates interactions between DM and quarks. Breaking the baryonic gauge symmetry generates the new particle masses and a small splitting between two DM states, while a residual symmetry keeps the lighter state stable. We identify regions compatible with the LZ candidate, the observed DM abundance, and current ATLAS and CMS dijet constraints. Within the scanned domain, these regions span DM masses $m_\chi\simeq0.19$-$4.5$ TeV, mediator masses $M_{Z_B}\simeq0.05$-$5.0$ TeV, and gauge couplings $g_B\simeq0.004$-$0.74$, with correlated values of these parameters. A representative thermal solution has $m_\chi=1$ TeV, $M_{Z_B}=1.44$ TeV, $g_B\simeq0.228$, and a mass splitting of $300$ keV. A small electroweak mixing allows the heavier DM state to decay rapidly, suppressing unwanted signals from its surviving population. This interpretation can be tested through complementary measurements: additional LZ and XENONnT data can establish whether the high-energy recoil signal persists, ATLAS and CMS Run-3 dijet searches can probe the mediator mass and coupling, and a dedicated IceCube analysis of four-quark final states can test DM capture and annihilation in the Sun. Together, these measurements can test complementary parts of the surviving region and assess whether the LZ candidate is consistent with this interpretation.

We study codimension-two conformal defects for massless fermions that are free in a four-dimensional bulk, but interact on a two-dimensional defect. The bulk Dirac equation strongly constrains defect conformal field theory data: it fixes the dimensions of operators in the bulk-defect operator product expansion and, for bulk-defect-defect three-point functions, enforces a double-twist relation when only one member of a shadow pair is allowed by unitarity. The lowest modes of monodromy defects provide an important exception, since both shadow partners can be unitary and their three-point functions are instead related by a shadow transform. We illustrate these structures with defect interactions, including an exactly tractable bilinear flow and Gross-Neveu-type quartic couplings. At a perturbative mixed fixed point, we find an explicit interacting example in which the double-twist condition is violated and the two shadow channels combine to give a regular bulk-defect-defect correlation function.

In de Sitter static patch holography, coupling bulk quantum fields to an observer's dynamical clock yields a type II$_1$ von Neumann algebra $\mathcal{M}_+$ of gauge-invariant observables. However, the unique tracial state on this algebra fails to reproduce semiclassical bulk correlation functions. We resolve this issue by introducing a family of heavy-clock states, representing an observer reference frame with heavy inertia. We prove that in the heavy-clock limit, $n$-point correlation functions of gauge-invariant dressed observables reproduce the bulk quantum field correlation functions on de Sitter spacetime. Furthermore, we investigate a generalized observer Hamiltonian $\widehat{H}_{\rm obs}=|\widehat{\pi}|$ that incorporates both forward-running ($\pi\geq 0$) and backward-running ($\pi <0$) clocks. The resulting von Neumann algebra $\mathcal{M}$ of gauge-invariant observables remains a type~II$_1$ factor and is isomorphic to $\mathcal{M}_+\otimes M_2(\mathbb{C})$, where $M_2(\mathbb{C})$ is the algebra of $2\times2$ complex matrices transforming between the two clock orientations. Time-reversal symmetry is implemented in this setting as an anti-unitary operator that exchanges the two clock orientations, yielding a type~II$_1$ von Neumann algebra $\mathcal{F}$ of gauge-invariant, time-reversal-invariant observables. We generalize the heavy-clock state construction to both $\mathcal{M}$ and $\mathcal{F}$, showing that $n$-point correlation functions calculated in heavy-clock states match the corresponding semiclassical bulk correlation functions. Finally, by coupling Einstein gravity to the Brown–Kuchař dust field, we derive the observer Hamiltonian $\widehat{H}_{\rm obs}=|\widehat{\pi}|$ from a perturbative reduction along the observer's worldline in the $G \to 0$ limit. This provides a field-theoretic foundation for the observer model developed in this work.

Global monopoles can carry electric charge even when the scalar field that forms them is neutral. We show that a CP-odd operator in the Goldstone effective theory, typically discarded as a total derivative, gives them an electric charge $Q=-Cn$, with $C$ its Wilson coefficient and $n$ the winding number. This is a Witten effect on a global defect, generated by a mixed $\theta$-term between electromagnetism and a composite connection built from the Goldstone fields. The same group theory condition that allows the operator also guarantees the existence of monopoles. We also give a fermionic UV completion and determine the coefficient by matching the Goldstone-Wilczek current.

We develop a homotopical framework for understanding the space of quantum spin systems based on topological $n$-nets, which assign associative unital algebras to local regions in an $n$-dimensional space in a manner that captures the locality structure of the underlying lattice theories. The net-theoretic perspective admits a natural categorification, in which the category of topological $n$-nets carries the structure of a higher Morita category. Moreover, the nets of greatest physical interest form a Karoubi-complete subcategory that shares many of the characteristic structural features of the category of finite TQFTs. Our main result identifies the group of locality-preserving symmetries of (3+1)-dimensional quantum spin systems (i.e. quantum cellular automata modulo stabilization, finite-depth quantum circuits, and translations) with the full Witt group of nondegenerate braided fusion categories, thereby answering a question posed by Haah.

Unless the tensor to scalar ratio is small enough, the non-adiabatic mode associated with the ultralight bosons may be dangerously comparable with the adiabatic spectrum of curvature inhomogeneities. We point out here that this statement depends on the timeline of the post-inflationary expansion rate. Provided the decelerated evolution is slower than radiation for a sufficiently long period, the relative weight of the non-adiabatic and adiabatic components does not conflict with the direct constraints coming from the large-scale observations. Conversely the presence of ultralight bosons excludes the presence of long stages expanding faster than radiation. The synthesis of the light nuclei and the spectrum of the relic gravitons at high frequencies set the relevant constraints on the duration of the decelerated stages, on the delayed dominance of radiation and on the mass range of the ultralight scalars.

We determine a universal sector of the spectrum of light operators in four-dimensional $\mathcal{N}=1$ class $\mathcal{S}$ superconformal field theories arising from M5-branes wrapped on a compact hyperbolic Riemann surface $\Sigma_2$. We work at large $N$, analysing Kaluza–Klein fluctuations about the dual Bah–Beem–Bobev–Wecht anti-de Sitter backgrounds for general values of the twist parameter $z$. To obtain these spectra, we specialise recently derived mass operators to modes that are constant on $\Sigma_2$ by imposing a suitable $z$-dependent generalised $G$-structure. We then organise the resulting eigenstates into long and protected $\mathcal{N}=1$ supermultiplets with definite flavour quantum numbers. As $z$ varies, rich patterns emerge in the spectrum, including both isolated multiplets and infinite towers of multiplets, which we characterise analytically.

The LZ 248 keV recoil candidate admits an interpretation in terms of pseudo-Dirac dark matter with a mixing-suppressed inelastic $Z$ interaction. In the MSSM, the Higgsino limit conflicts with the adopted solar-neutrino bound, while a gaugino realization requires an unprotected mass degeneracy. We realize such spectra in the MRSSM, where an $R$-symmetric Dirac bino produces the required $Z$ transition and wino coannihilation supplies the observed relic abundance. We impose the Higgs and gauge coupling relations of $N=2$ supersymmetry at a high scale and evolve them to low energy. With the remaining model parameters held fixed, we obtain spectra spanning roughly 300-850 GeV that satisfy the adopted constraints and have a small diagonal axial current. If anomaly mediation dominates the Majorana splitting, its local scale is tens of MeV for splittings of a few hundred keV. A five-dimensional warped construction generates this scale through Goldberger-Wise stabilization and a loop correction to the no-scale Kähler potential. The spectra remain testable through elastic scattering, solar neutrinos and long-lived charged states.

We study how mixed-state correlations reorganize across island transitions in Jackiw-Teitelboim gravity coupled to a non-gravitating bath. Using the partial-dimensional-reduction realization of double holography, we compute reflected entropy for adjacent and disjoint radiation regions in the vacuum and in the thermofield-double state of an eternal black hole. Reflected entropy probes the internal partition of the entanglement wedge and therefore resolves structure that is invisible to the ordinary Page curve: its dominant saddle can change even when the entropy saddle of the union remains fixed, and it vanishes at leading order when the entanglement wedge disconnects. We show that the lower-dimensional reflected-island description agrees, to leading order in the dynamical brane fluctuation, with the higher-dimensional defect-extremal-surface picture. The finite-angle comparison further suggests a projection-covariant identification of island and brane endpoints at linear order. The resulting Page-like curves and Markov gaps provide a geometric probe of the reorganization of the purification and of non-Markovian, multipartite correlation structure during island transitions.

The $q$-deformed Weil-Petersson volumes of Do and Norbury are the top-degree parts of Okuyama's discrete volumes, which are defined by topological recursion on the spectral curve of the double-scaled SYK (DSSYK) model. We show that the same q-deformed volumes can be obtained from a double-scaled matrix model whose disk density is found by zooming in on the soft edges of the DSSYK density. Applying the same procedure to the hard edge of $\mathcal{N}=1$ DSSYK, we obtain candidate $q$-deformed $\mathcal{N}=1$ super Weil-Petersson volumes. They are polynomials of fixed degree, and they reduce to the $\mathcal{N}=1$ super Weil-Petersson volumes in a scaled $q\to1$ limit. These candidate volumes differ from the $\mathcal{N}=1$ volumes of Do and Norbury in (arXiv:2510.12431) up to what we call "irrelevant" contributions which exactly vanish in the scaled $q\to 1$ limit. Together, these results demonstrate how q-deformed volumes can be naturally associated to the spectral edges of various DSSYK models and provides an intuitive way to construct them in supersymmetric contexts.

We construct a set of conserved charges which are deformations of quantum KdV charges. They are associated with the modular transformation of a GGE with the spin-$\sigma$ KdV charge inserted with chemical potential $\alpha_\sigma$. The charges are formal power series in the chemical potential, with coefficients given by local integrals of motion. We define local recursion relations and equivalent flow equations, prove commutativity to all orders, and establish uniqueness of the currents modulo total derivatives for a fixed generating series. We show that the eigenvalues of these deformed charges can be obtained from the thermodynamic Bethe Ansatz in two models. In the $c=1/2$ free fermion theory, the deformed charges reduce to explicit linear combinations of undeformed KdV charges, and their ground-state eigenvalues agree with the TBA expansion to all orders. In the Lee-Yang model, we find numerical agreement through cubic order in the spin-$5$ deformation for the first few charges evaluated on low-lying states.

Contemporary large-scale structure analyses center around the galaxy power spectrum, modeled with one-loop perturbation theory. This description naturally breaks down at large wavenumbers, prohibiting the extraction of cosmological information from small-scale clustering. In this work, we present a complete model for the redshift-space galaxy power spectrum up to two-loop order, derived in the framework of the Effective Field Theory of Large Scale Structure. This accounts for a wide variety of effects, including fifth-order galaxy bias, redshift-space distortions, small-scale non-linearities, spatial non-locality, long-wavelength bulk flows, coordinate distortions, and stochasticity, involving a total of 49 free coefficients. Our model additionally encodes all deterministic contributions to the one-loop bispectrum and trispectrum (as well as the tree-level quadspectrum and pentaspectrum), which depend on many of the same parameters. We implement the model numerically, using the vegas algorithm to precompute the loop integrals; this allows the full likelihood to be evaluated in milliseconds. The approach is validated using power spectra measured from high-resolution simulations, considering both dark matter and realistic galaxy samples. The extension to two-loop order greatly increases the range of scales over which the power spectrum can be modeled, with $k_{\rm max}$ rising from $0.2h\,\mathrm{Mpc}^{-1}$ to $0.34h\,\mathrm{Mpc}^{-1}$ for a luminous red galaxy sample at $z=0.5$. Much of the additional information is absorbed by the numerous fifth-order biases and counterterms; for this reason, constraints on $\sigma_8$ are not significantly enhanced by the inclusion of two-loop terms. Future work will assess the full implications of the two-loop model for cosmological parameter inference, both alone and in combination with higher-order statistics.

The Relativistic Continuous Matrix Product State (RCMPS) ansatz introduced in arXiv:2102.07741 is a translation-invariant variational ansatz intended to approximate the ground states of gapped one-dimensional relativistic Quantum Field Theories directly in the continuum limit and in infinite volume. In this work, we develop an ansatz, referred to as the Relativistic Quasiparticle (RQP) ansatz, for the low-lying one-particle excitations of the RCMPS vacuum, as well as for solitons interpolating between two distinct degenerate vacua. The corresponding energies of these states can be obtained as the eigenvalues of an effective Hamiltonian. The RQP ansatz generalizes constructions used in the Matrix Product State and Continuous Matrix Product State literature. We apply the RQP ansatz to the sine-Gordon model and find good agreement with results from integrability for both the soliton and breather masses. We also apply the RQP ansatz to the $\phi^4$ theory, in both its $\mathbb Z_2$-preserving and $\mathbb{Z}_2$-broken phases, and determine the spectrum of particles and solitons. This enables us to determine the parameter regime for which multiple stable particles exist.

We construct an exact stationary axisymmetric vacuum configuration in metric affine Kalb-Ramond gravity with zero cosmological constant. Independent variation of the metric, connection, and antisymmetric field yields the complete field equations and the algebraic relation between the physical and auxiliary geometries. A Kerr auxiliary metric and a closed corotating vacuum two form of fixed positive norm determine the physical metric. The tensor kernel contains the horizon generator, and the metrics, independent connection, and vacuum field share a smooth extension across the nonextremal physical Killing horizon and the rotation axes at finite radius for unequal deformation factors. We obtain an explicit sufficient domain for a causal exterior and an asymptotically locally flat end at fixed nonpolar angles. The physical Hamiltonian yields the timelike and null equations, equatorial effective potentials, circular orbit properties, radial stability, and perihelion advance. Numerical photon evolution determines the critical curve on an orthonormal observer screen. Its size, shape, and centroid depend on $\epsilon=\xi_2b^2/[2(1+\xi_1b^2)]$ at fixed normalized mass scale and spin, with Kerr recovered at $\epsilon=0$. Geometric observations probe this combination and retain an exact degeneracy between the curvature couplings. A static equatorial comparison with Mercury gives a conditional sensitivity of $2.30\times10^{-11}$ for $|2\epsilon|$ under the stated angular convention and mass setting.

We study the spectrum of two-particle bound states of Kähler-Dirac fermions coupled via gravity in Euclidean Dynamical Triangulations (EDT). We work in the quenched approximation, where the geometry is allowed to fluctuate, but there is no back-reaction from the matter on the geometry. The Kähler-Dirac action respects an exact $U(1)$ symmetry that is related to continuum chiral symmetry, and this $U(1)$ symmetry ensures that some of the bound-state masses vanish in the chiral limit of vanishing fermion bare mass. The bound-state masses that are not protected by the $U(1)$ symmetry do not vanish in the chiral limit, but the scale associated with the symmetry breaking does not appear to be a physical scale like the Planck mass or the curvature scale of the emergent de Sitter background. Rather, the mass scale associated with this non-degeneracy appears to be a positive power of the lattice spacing, decreasing as the continuum limit is approached. This suggests that Kähler-Dirac fermions in EDT can be interpreted as the gravity analog of staggered fermions in flat-space lattice field theories, with similar behavior.

We establish that bond Hamiltonian densities, up to local difference terms whose sum vanishes under periodic boundary conditions, lying in the commutant of bond operators, $w_j\pm w_{j+1}$, is a necessary and sufficient condition for a one-dimensional nearest-neighbour Hamiltonian to conserve a uniform or staggered sum of the one-site operators $w_j$. Starting from these local commutants, we show that every such Hamiltonian and its conserved charge can be obtained from monodromy matrices constructed using regular and non-regular members of scalene Yang-Baxter triples. The results hold on periodic chains of length $L\geq3$, with even length required in the staggered case. The results do not require translation invariance, and hence the interaction on each bond can be chosen independently from the full corresponding commutant. Our representation-independent construction applies in arbitrary finite local dimension and exhausts the Hamiltonians with either prescribed additive symmetry, without requiring ordinary Yang-Baxter integrability. We illustrate the construction with spin-$\tfrac12$ and spin-1 systems and discuss its relation to the double-commutant theorem. Classifying the one-site generators $w$ and their associated bond commutants provides a route to classifying such Hamiltonians with additive conserved charges.

A novel physics-informed neural networks (PINNs) based approach for solving functional renormalization group flow equations is presented. We investigate the finite temperature phase transition in $O(N)$ models without relying on the large-$N$ approximation, which was used in earlier attempts with similar methods. We argue that these previous solutions cannot easily be generalized for more complex symmetries, and hence our approach can provide new insight. Our technique relies on a series of ansätze that combines the small- and large-field approximation schemes with a neural network, leading to a highly accurate approximation over the entire field range. We compare the PINNs approach with traditional grid-based Runge-Kutta results and show that the network can successfully learn the temperature, field, and scale dependencies of the effective potential in the local potential approximation.

If cosmic acceleration is driven by a positive cosmological constant, the universe approaches an eternally accelerating de Sitter state, whose interpretation in quantum gravity remains elusive. We develop a framework in which acceleration is instead a transient stage of dark-sector relaxation towards compositional equilibrium: matter and dark energy approach a stationary density ratio, eventually diluting like pressureless matter. Guided by linear response theory and Onsager's near-equilibrium regression hypothesis, we describe this evolution through a composition variable measuring departure from equilibrium. Extending constant fractional relaxation to the full background evolution yields the dark-energy equation of state $w=w_0a^{-n}$, where $n$ is the relaxation rate per e-fold of expansion. This history connects early dark-energy suppression, an upward phantom crossing and a density maximum to a pressureless scaling future. Using DESI DR2 BAO and Planck distance priors, with and without three alternative supernova compilations, we find a nominal $2.6$–$3.6\sigma$ preference for nonzero relaxation over constant $w$. The composition framework also motivates a constitutive prescription for linear perturbations that remains regular at phantom crossing. Near equilibrium, regular long-wavelength composition disturbances relax at the background rate to leading order, while small-scale fluctuations propagate as damped sound waves. We prove, however, that for separately conserved matter and dark energy, the pointwise constitutive relation cannot sustain a regular, gradient-stable negative-pressure branch throughout its full past evolution. We explore modifications of the pressure response and their consistency with neighbouring homogeneous histories, identifying requirements for extending the near-equilibrium description to the full cosmological evolution.

We investigate the anomaly-induced transport properties of a holographic superconductor exhibiting spontaneous symmetry breaking. The holographic model incorporates vector and axial gauge fields, an additional non-anomalous $U(1)$ symmetry, and a charged scalar field that drives the phase transition. Working in the probe limit, we numerically construct the superconducting background under two alternative scalar field quantizations, corresponding to operators with scaling dimensions $\Delta=1$ and $\Delta=3$ (denoted as the $O_1$ and $O_2$ theories, respectively). Using Kubo formulae, we compute the chiral magnetic conductivities and examine their response to the scalar condensate. Our findings demonstrate that spontaneous symmetry breaking allows anomaly-induced transport to extend beyond anomalous currents, significantly impacting the non-anomalous sector as well. Remarkably, this effect appears in both theories, indicating that the influence on the non-anomalous sector is independent of the chosen quantization. The comparison of our numerical results with the analytical limits for $O_i \to 0$ and $O_i \to \infty$ $(i=1,2)$ reveals consistent behavior across both theories.

We introduce a discrete spectral curve from $\mathscr{N}=2$ double-scaled SYK whose topological recursion defines quasi-polynomial volumes in integer boundary lengths. The curve has two edge theories: a local $\mathscr{N}=2$ theory at the lower edge and a bosonic theory at the upper edge. Focusing on the local $\mathscr{N}=2$ theory, we compute its finite-$q$ volumes and independently check the first few using the string equation. In the $q\rightarrow 1$ continuum limit, these recover the super Weil-Petersson volumes of Turiaci and Witten. Finally, we give an all-genus intersection-theoretic interpretation of these local volumes on the moduli space of stable marked curves, in terms of a deformed spin class with a gap-dependent $\kappa$-class dressing.

We complement and extend our recent study of the non-linear evolution of the Gregory-Laflamme instability of black strings in Einstein-Gauss-Bonnet gravity in five spacetime dimensions. First, we study time-dependent perturbations of uniform black strings in Einstein-Gauss-Bonnet theory and determine the growth rates as a function of the coupling. We find that for positive Gauss-Bonnet couplings, the black strings are more unstable than in general relativity in the sense that the growth rates are larger and shorter wavelengths are unstable. In the second part of the paper we show that the hyperbolicity of the equation of motion of Einstein-Gauss-Bonnet theory is determined by an effective metric when the dynamics is restricted to spherical symmetry in the asymptotically flat directions. When the effective field theory becomes strongly coupled, as it happens near the endpoint of the Gregory-Laflamme instability of the black string, this effective metric becomes degenerate and the Cauchy evolution breaks down. Applying this criterion to uniform black strings, we find that for any positive Gauss-Bonnet coupling there is an open set of regular solutions (including the one of minimal thickness) on which the effective metric degenerates in a neighbourhood of the horizon. Therefore, we argue that these solutions cannot be attained from weakly coupled initial data by Cauchy evolution and the solutions of the linearized equations around them cannot be interpreted as approximations to nearby non-linear evolutions. We provide further evidence for this picture with non-linear simulations of the Gregory-Laflamme instability. The non-linear simulations terminate through a loss of hyperbolicity of the Tricomi or Keldysh type, depending on the sign of the Gauss-Bonnet coupling.