Papers

First law consistency alone does not determine the black hole state space of NUT-charged spacetimes, because several inequivalent macroscopic formulations can yield consistent thermodynamics. We develop a two-horizon sector diagnostic for the electrically charged Kerr-Newman-NUT family by organizing the inner- and outer-horizon entropies and inverse temperatures into sum ($\Sigma$) and difference ($\Delta$) sectors. The charged rotating geometry gives a more stringent test of the uncharged Taub-NUT sector result, since the mass $M$, ordinary electric charge $Q$, ordinary angular momentum $J$, NUT charge $N$, and the NUT secondary hair $J_N=MN$ all enter the same two-horizon thermodynamics. For the physically anchored minimal homogeneous state spaces defined and tested here, we find a clear sector separation: the $\Sigma$ sector closes with the charge-like variables $Q$ and $N$, whereas the $\Delta$ sector additionally requires the rotation-like variables $J$ and $J_N$. Natural reductions that eliminate either $J_N$ or $N$ fail to reproduce the first law coefficient fixed by the sector temperature, and their associated Bekenstein-Smarr relations do not close with the assigned scaling weights. Within this class, electric charge and ordinary rotation therefore do not absorb the NUT secondary response, and the charged rotating family supports the NUT bi-hair organization: $N$ has a charge-like sector role, while $J_N=MN$ is a rotation-like thermodynamic secondary hair. The latter is defined off shell in the homogeneous equation of state, not as a new metric parameter or asymptotic conserved charge.

We investigate the Fulling-Davies-Unruh effect in a local Lorentz-violating effective field theory, focusing on the quantum-field response of accelerated detectors. We canonically quantize a real scalar field exactly in the coefficients for Lorentz violation. The dispersion relation, Hamiltonian, and massless and massive Wightman functions are obtained. We determine the conditions under which the scalar dynamics preserves boost symmetry and distinguish these from the weaker conditions required for stationarity along a single accelerated worldline. The Wightman functions are used to construct the finite-time Unruh-DeWitt response for a uniformly accelerated detector. For generic coefficients the response is nonstationary and depends on both the duration and temporal location of the measurement. The spectrum, which is the resulting excitation rate as a function of the energy level difference in the detector, is obtained numerically. It shows discernable differences with the usual massive thermal spectrum for dimensionless coefficients on the order of $10^{-7}$. Experimental implications of the result are discussed. As an alternative viewpoint, we place Lorentz violation in the point-particle sector, derive the exact trajectory generated by a constant electric field, and study the proper-time Fourier response of a conventional scalar wave along the modified trajectory.

We construct exact, static, circularly symmetric charged regular AdS$_3$ black hole solutions in a three-dimensional scalar-vector-tensor theory obtained from regularized Gauss-Bonnet couplings. While the Maxwell-charged counterpart of this theory suffers from a logarithmic curvature singularity at the origin, we demonstrate that coupling the action to non-linear Born-Infeld electrodynamics cures this pathology. We obtain the metric function and show explicitly the regularity of the core. Depending on the choice of parameters, the solution exhibits various horizon structures, including single-horizon, double-horizon, extremal black holes, and horizonless regular geometries. Finally, we discuss the significance of this regular spacetime as a testbed for microscopic entropy calculations in singularity-free setups.

We prove that 3d Lovelock gravity, the Horndeski theory obtained from the regularized Lovelock invariants in three dimensions, admits a holographic c-theorem at all orders and for arbitrary values of the couplings. In the minisuperspace of domain wall solutions, the equation of the Horndeski scalar is a total derivative at every order, which locks the derivative of the scalar to that of the warp factor along the flows we consider and allows the null energy condition to be integrated into a monotonic c-function. The linear scalar profile of the resulting vacuum breaks the special conformal transformations, so the dual theory is scale-invariant but not conformal, and the central charge is defined as the coefficient of the logarithmic divergence of the on-shell action on the sphere. We compute it exactly for the Gauss-Bonnet case and asymptotically for the full tower, and find that it is linear in the couplings and matches the UV value of the c-function. Since all results depend on the couplings only through two generating functions, we give the resummed Lagrangians, c-functions and central charges in closed form for the choices of couplings that lead to regular black holes, and classify the resummed theories by the positivity of the effective Newton constant on the vacuum and the uniqueness of the vacuum with a non-trivial scalar.

Low-frequency Drude response does not by itself determine which nearly conserved sector carries an electric current. We classify the leading cubic retarded response of an isolated, inversion-symmetric slow vector by its pole topology. Constitutive nonlinearity produces only incoming-frequency poles, whereas nonlinear relaxation adds a propagator at the emitted frequency; coupling to a second scalar slow mode generates pair-frequency poles. We then compute the full complex third-harmonic response of finite-density Dirac–Born–Infeld probe branes in Lifshitz black-brane backgrounds. In the marginal $z=2$ theory, the dense infrared response approaches the relaxation topology, with a signed infrared weight $p_{\rm IR}=0.994\pm0.002$ and a normalization-independent zero at $\omega_\times/\Gamma_J=0.2918$. Nonmarginal $z=1$ and $z=3/2$ backgrounds instead realize mixed constitutive–relaxation weights, demonstrating that the topology is selected dynamically rather than imposed by the DBI square root. The exact nonlinear dc solution further yields a parameter-free dense-limit scaling function and a crossover field $E_{\rm nl}\propto T^{3/2}$ at $z=2$. These results connect emergent higher-form slow currents, nonlinear response theory, and holographic transport, while the two-mode extension identifies the additional pole structures expected when energy or deformation modes remain slow.

We investigate Hawking radiation of a quantum-corrected Schwarzschild black hole with vacuum polarization and conformal anomaly effects. The corrected geometry has two horizons, a non-monotonic Hawking temperature that vanishes at a critical mass, and a logarithmic entropy correction. We compute greybody factors, spectra, and emission rates for massless bosonic fields of various spins and angular momenta. Quantum corrections suppress low-energy greybody factors and enhance high-energy ones. During late evaporation, where quantum influences become significant, the decreasing temperature strongly suppresses emission. In this case, the higher-spin modes become negligible, and the scalar $s=l=0$ mode dominates. The black hole lifetime is greatly extended as it asymptotically approaches a stable extremal remnant.

The compact four-dimensional manifold $\mathbb{CP}_2\# 3\overline{\mathbb{CP}_2}$ is known to admit a toric Kähler-Einstein metric $g_{\text{KE}}$, but the metric is not known in closed form, which makes it difficult to draw conclusions about its geometry. In this article, we use a combination of analytic and computer-assisted techniques to produce an approximate Einstein metric $g$ described explicitly herein, and also prove that the true Einstein metric $g_{\text{KE}}$ is close to $g$, where both the closeness and the topology are described explicitly. As an application, we prove bounds on the first invariant eigenvalue of the Laplace-Beltrami operator, and prove that this Kähler-Einstein metric does not have positive holomorphic sectional curvature everywhere.

The problem of thermal equilibrium in general relativity is discussed and the unique role played by the fluid associated with the cosmological constant is emphasized. In addition to being the only fluid that is always in thermal equilibrium, it is shown here that its energy can also be seen as a universal quantity given by $E_\Lambda=\rho_\Lambda V$, where $V$ is a spatial volume. Furthermore, if the cosmological constant turns out to be a universal constant, then the conclusion that any spatial volume $V$ has an intrinsic energy follows naturally from the approach considered here. A possible application to quantum theories of gravity that postulate the existence of a minimal length scale is discussed. In studying the energies, the so-called teleparallel equivalent of general relativity is used, and the difficulty with the zero-point energy is discussed in light of the gravitational energy problem. The quasi-local energies of the Reissner-Nordström-de Sitter black hole and of a regular black hole are calculated. The results obtained here with the teleparallel theory are consistent with our expectations.

In this paper, we study the evolution of curvature and entropy perturbations in three-field inflation with non-canonical kinetic terms. Using the kinematic basis in field space, we characterize the background trajectory through its turning rate and non-planar torsion. We also emphasize the inherited structure of perturbations from the kinematic system, which detaches the distinct roles of turning rate and torsion in the interactions among perturbations. We present and study numerically a three-phase model with an intermediate decelerated expansion stage in which two separated transient epochs amplify two distinct families of modes, generating a double-peaked curvature power spectrum. This double-peaked power spectrum leads to the formation of primordial black holes with two characteristic masses, $M_1\sim2\times10^{-12}M_\odot$ and $M_2\sim52M_\odot$ explaining, simultaneously, both dark matter and the LIGO-Virgo-KAGRA binary black hole mass range.

A spectator spin-2 field can mix linearly with the metric tensor perturbations. We study the coupled tensor system in an inflationary background, including a parity violating effect parametrised by $\theta$. Without expanding in the linear mixing between the two fields, we solve the system exactly for arbitrary mass while treating the mixing strength nonperturbatively. The mode functions of both helicities are constructed by acting with an operator-valued Gauss hypergeometric function ${}_2F_1$ on Whittaker modes, and the late-time power spectrum of each graviton helicity is expressed in closed form in terms of the generalised hypergeometric function ${}_3F_2$. We find that one helicity is exponentially enhanced, showing that strong mixing with a spectator spin-2 field can generate a large and highly chiral primordial gravitational wave spectrum. The degree of circular polarisation is bounded by $\tanh(\pi\theta)$, independently of the spin-2 mass and the mixing strength. The same solution also gives the late-time power spectrum of the spectator field and its cross spectrum with the graviton. In the weak mixing limit, our exact result reproduces the perturbative Schwinger-Keldysh result. These solutions provide a nonperturbative framework for studying primordial gravitational waves sourced by additional tensor modes.

We study the effects of the moat regime on meson and quark correlation functions and the quark-antiquark potential in low-energy QCD, building on the two-flavor quark meson model in a random-phase approximation. We investigate the relation between the moat regime and Friedel oscillations in the quark-antiquark potential at large density and zero temperature. As it turns out, oscillations from the moat regime are a distinct phenomenon, arising from poles on unphysical Riemann sheets in this region. Furthermore, we find that in addition to pions and the sigma meson, also other mesons, including vector mesons and the eta, are sensitive to the moat regime. This leads in particular to an enhancement of the meson spectral function in the spacelike region. The quarks, on the other hand, appear to be essentially insensitive. This can have far-reaching consequences for the phase diagram, as for example the chiral phase boundary, including the location of the critical endpoint, can be affected in the moat regime even in absence of inhomogeneous instabilities.

The planar loop equations of a Hermitian one-matrix model leave finitely many low moments undetermined. Hankel positivity constrains these moments but does not reveal how a fixed multicut family is embedded in moment space. We introduce a finite-plane diagnostic using the Cauchy kernels $f_n(x)=(z_n-x)^{-1}$ which we use as spectral probes. Their Gram matrix is the positive-semidefinite Pick matrix $P_{mn}$, whose positivity defines a finite-node bootstrap analogous to the Hankel bootstrap. For a fixed regular multicut topology, the nonbranching double zeros of the spectral discriminant, which we call dressed saddles, impose transverse constraints on the corresponding moment-space locus, while its remaining directions are filling fractions. Writing $z=E+i\eta$, $E$ selects a spectral region and $\eta>0$ sets a continuous resolution scale. We use $P(z,z)$ as a finite-plane spectral response and interpret $\nabla_{\mathbf m}P(z,z)$ as a moment-space susceptibility. Near a regular real dressed saddle, this susceptibility is enhanced as $\eta^{-2}$ and aligns with a conormal to the filling-fraction manifold, whereas the leading enhancement cancels along tangent deformations. Responses near several independent saddles can therefore reconstruct the conormal space and, through their common kernel, its tangent space. Combining Pick positivity with reality and analyticity of the resolvent, we obtain alternative analytic derivations of known planar results in quartic and sextic models. The asymmetric quartic makes the one-dimensional filling-fraction geometry explicit, while sextic models exhibit independent conormal directions. These results clarify how local consistency conditions constrain the low moments before global period matching and the equilibrium variational inequality select the equilibrium measure.

1+1D symmetry-protected topological (SPT) phases with invertible symmetry can be characterized by the symmetric entanglers: globally symmetric finite-depth local unitary circuits that generate representative ground states from a product state. For non-invertible symmetries, however, distinct SPT phases, such as the three $\mathrm{Rep}(D_8)$ SPT phases, may not be connected by any symmetric entangler. We show that the three $\mathrm{Rep}(D_8)$ SPT phases can nevertheless be connected by symmetry-permuting finite-depth local unitary circuits, realizing dualities predicted by topological quantum field theory (TQFT). We construct an explicit matrix product unitary connecting two of the $\mathrm{Rep}(D_8)$ SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.

The chiral soliton lattice (CSL) is conventionally described as a periodic winding configuration of a compact scalar field. In this paper, we formulate the CSL in a higher-form framework based on a Stückelberg coupling between a two-form gauge field $C_2$ and a three-form gauge field $A_3$, in which strings and walls can be treated directly as extended sources. Higher-form gauge invariance requires the string worldsheet to be the boundary of the wall worldvolume. In the quadratic dual effective theory, exchange of the massive higher-form mode generates a repulsive Yukawa interaction between parallel walls. With its coefficient fixed by duality, the resulting CSL lattice spacing agrees well with the exact Sine–Gordon result without parameter fitting. We then extend the description to a nonlinear, multi-branch higher-form theory. It reproduces the exact dilute wall–wall interaction coefficient, the periodic CSL and its energy-minimization condition, as well as the gapless CSL phonon. The phonon is identified as a collective displacement of the periodic higher-form background, while scalar winding is reinterpreted as branch flow of the nonlinear higher-form theory.

We study the gravitational collapse of a spherically symmetric, inhomogeneous dust cloud in five-dimensional AdS Chern–Simons gravity. Working in the torsion-free sector and using comoving Lemaître–Tolman–Bondi coordinates, we derive the reduced field equations and obtain an exact collapsing interior solution. The areal radius evolves periodically in time, but the physical collapsing branch extends only up to shell focusing or an earlier loss of regularity, while the initial density determines a radial function whose square is proportional to the conserved quasilocal mass. This separates the roles of the initial velocity and density profiles in controlling shell focusing and trapping. We derive conditions for central regularity and for avoiding shell crossing, analyze the Kretschmann scalar, and show that shell focusing corresponds to a genuine curvature singularity, the weak and strong energy conditions are preserved throughout the regular collapsing phase. The homogeneous limit reduces consistently to a five-dimensional FLRW interior. The collapsing cloud is matched smoothly to the black-hole branch of the static AdS Chern–Simons exterior. The null expansions show that a finite-radius apparent horizon forms only when the quasilocal mass exceeds a critical threshold. Initially untrapped shells above this threshold become trapped before shell focusing, whereas below the total-mass threshold no finite-radius future-trapped symmetry sphere forms in the regular interior.

We present and study a family of exact Taub-NUT-AdS solutions with scalar hair in four-dimensional ${\cal N}=2$ gauged supergravity. The solutions are supported solely by a nontrivial scalar field and its self-interaction potential, with all gauge fields switched off. We determine the conditions under which Killing horizons exist and demonstrate that the spacetime admits at most one Killing horizon, and whenever it exists it is necessarily nondegenerate. In particular, the NUT deformation can give rise to a horizon in a branch whose static limit is horizonless. We also establish that the solutions with nontrivial scalar hair admit no Killing spinors. As in ordinary Taub-NUT-AdS spacetime, the global structure is afflicted by closed timelike curves. We compute the conserved mass using the covariant phase space method and formulate a restricted first law with the NUT parameter held fixed. Finally, we study the Euclidean sector, including an exceptional family specific to Euclidean signature, and determine the regularity conditions for bolts and nuts.

We introduce a transformer reinforcement learning algorithm that learns to solve high loop-level scattering amplitudes in planar N = 4 Super Yang-Mills theory. Our algorithm improves on previous transformer-only results by incorporating previously derived symmetries and relationships into the learning algorithm. This results in a greatly decreased fraction of the solution that needs to be known a priori to solve the entire problem. An additional benefit is that our algorithm also ensures that every output obeys the set of known relationships. Rather than predicting all coefficients independently, the model proposes assignments that are propagated through exact linear relations, while MCTS searches over assignments when propagation alone is insufficient. This is crucial to the generalization of machine learning approaches to higher loops, as without this, there is no way to overcome the factorially scaling of state sizes and compare to results derived via other methods. Using the symbology representation of the form factor, we frame the problem as learning a mapping between discrete sequences and integer coefficients.

One examines a codimension-one thick braneworld in the scalar representation of $f(Q,B)$ gravity, where $Q$ is the nonmetricity scalar, and $B$ is the boundary term satisfying $R=Q-B$. We write the gravitational sector in terms of two auxiliary scalar fields, $\varphi=f_Q$ and $\psi=f_B$, and an interaction potential $U(\varphi,\psi)$ obtained by a Legendre transformation from the $f(Q,B)$ function. Working in the coincident gauge and assuming a five-dimensional warped geometry with four-dimensional Poincaré symmetry, we derive the complete set of brane equations sourced by a canonical bulk scalar field. To accomplish our purpose, we address two models of smooth asymptotically AdS thick brane with localized scalar profiles. Furthermore, we also analyze tensor perturbations and demonstrate the localization and stability of the massless graviton.

In holography, analytically continued finite temperature correlation functions $G(t)$ exhibit signatures of the black hole singularity. These take the form of singularities at certain values of $t$ whose bulk origin is a null geodesic worldline "bouncing off" the black hole singularity. We study certain quantum corrections to this effect in 2D dilaton gravity that are captured by gravitational backreaction of the worldline onto the black hole geometry. These corrections smooth out the bouncing geodesic singularities. By following the backreacted geodesic saddle in a steepest descent analysis we find instead that the black hole singularity physics gets encoded in a subtle way involving a Stokes phenomenon near the coincident point singularity of $G(t)$ at $t=0$ (and its thermal image). We point out a parallel between the structure of Stokes lines uncovered in this analysis and the structure present in the analysis of forbidden singularities in large $c$ 2D conformal blocks. Finally we make some preliminary remarks about the significance of quantum corrections in these models beyond backreaction.

We derive the axion Weak Gravity Conjecture (aWGC) from the nonperturbative fragmentation of Euclidean wormholes into charged defects. Requiring fragmentation to lower the Euclidean action fixes the axion action-to-charge bound and its order-one coefficient. Without additional scalars, this coefficient coincides with that of the Imaginary Distance Bound (IDB), while additional scalars strengthen the bound. The aWGC in the presence of multiple axio-dilaton pairs is discussed, leading to geometric representations. Axions satisfying the aWGC render the corresponding wormholes unstable, potentially suppressing their proliferation and resolving associated factorization problems.

We study charged soliton branches in quasi-one-dimensional chiral magnetic systems with Dzyaloshinskii–Moriya (DM) interaction, easy-axis anisotropy, and Zeeman coupling. The same static magnetic functional is equipped with two different dynamical completions: an antiferromagnetic model with second-order time derivatives and a ferromagnetic model with Berry-phase dynamics. On the helical branch selected by the static DM interaction, the problem reduces to an analytically tractable one-dimensional system for the polar angle of the order parameter. We derive the existence conditions for polar Q-balls from the curvature of the reduced effective potential and the presence of a nonzero turning point. In the antiferromagnetic case, the allowed frequency window is symmetric and can be completely closed by the combined effect of the DM coupling and the Zeeman field. At zero Zeeman field, the same reduction also supports antiferromagnetic Q-kinks, for which we obtain explicit profiles, charges, energies, and reduced-sector fission criteria. In the ferromagnetic case, the Berry phase makes the rotation frequency act as a shifted Zeeman field. As a result, north- and south-pole charged droplets are selected by opposite signs of the shifted rotation. We also show that a formal pole-to-pole solution of the ferromagnetic mechanical problem does not generally correspond to a finite-energy magnetic soliton, because the Berry term does not renormalize the physical Hamiltonian. These results clarify how charged-soliton mechanisms depend on the underlying magnetic dynamics, even when the static chiral energy is the same.

In this thesis, we consider general relativity on a manifold with a timelike boundary of finite size, across all signs of the cosmological constant $\Lambda$. We impose conformal boundary conditions, whereby the conformal class of the induced metric and the trace of the extrinsic curvature $K$ are fixed at the boundary. In Lorentzian signature, we analyse the linearised Einstein equations about Minkowski, de Sitter (dS), and anti-de Sitter (AdS) space for a variety of boundaries, employing the Kodama-Ishibashi formalism adapted to manifolds with a boundary. In Euclidean signature, we study the thermodynamics of black hole and cosmological horizons enclosed by the boundary, computing the leading semiclassical approximation of the gravitational path integral, for which the boundary data define a conformal canonical ensemble of fixed conformal temperature and $K$.

A mass quench generates anomalous pair correlations that are absent from the final particle occupations. For a free real scalar field in $1+1$ dimensions, we define a bilocal observable by smearing the statistical Keldysh correlator with a Morlet kernel on the finite post-quench relative-time interval. Its excess over the dephased correlator gives a dimensionless relative coherence weight. At fixed momentum, this weight is exactly independent of the initial temperature for Gaussian thermal states evolved with the same free Hamiltonian: the common thermal amplitude cancels between numerator and denominator. The cancellation is not a purity criterion and is not exclusive to wavelets. We derive the finite-window response and show that the anomalous signal depends essentially on the observation window; an admissible zero-mean wavelet annihilates the relative-time-constant anomalous term on the full line. We compare this response with the signed finite-time Wigner spectrum and derive a distinct Gaussian-extension positivity bound. Exact smooth-quench occupations provide an independent dynamical reference. Finally, we formulate a renormalized Hartree extension and delimit the oscillatory and nonoscillatory regimes of a scalar mode on a fixed two-dimensional de Sitter background.

We study a family of locally excited states in two-dimensional conformal field theories in different setups, defined on the plane, on the cylinder, or at finite temperature. These states are constructed by assigning independent chiral and anti-chiral regulators to a local primary operator, leading to excitations carrying net momentum. We analytically calculate the first few Lanczos coefficients and the early time behaviour of the spread complexity associated with these states. Then, using numerical methods, we obtain the coefficients reaching larger Krylov indices and find the associated spread complexity for a longer range of time evolution. We also compare the rate of change of the resulting spread complexity with the proposed holographic dual quantity, related to the proper momentum of an infalling particle in the dual bulk, but we observe a mismatch.

We derive an exact background-dressed TGTG formula for the one-loop quantum vacuum inter- action between two semitransparent Dirac-delta plates in the one-soliton Pöchl-Teller background. The interaction is defined through a relative determinant in which the two isolated one-plate contributions are subtracted in the same background. As a result, the energy depends on the individual plate positions as well as on their separation. For repulsive plates, the normalizable zero mode does not induce an infrared divergence in the relative interaction energy. We also extend the construction to planar plates and analyze the corresponding position-dependent interaction forces.

Kerr black holes and electroweak sphalerons are remarkable solutions of two pillars of modern physics: General Relativity and the Standard Model of particle physics, respectively. In this work, we investigate their interplay by constructing nonlinear sphaleron clouds around Schwarzschild and Kerr black holes in the probe limit. We first revisit static and spinning (multi-)sphalerons in flat spacetime, using the measured electroweak parameters. We then explore the domain of existence and physical properties of the corresponding black-hole configurations, revealing a rich branch structure. Remarkably, the sphaleron clouds retain a finite mass gap and do not approach linear clouds within the families studied, distinguishing them from the familiar clouds associated with the onset of superradiant instabilities. We also obtain a closed-form leading-order Higgs solution on an exact Yang-Mills configuration in a Schwarzschild background.

A confluence of recent works has shown that many quantum circuits and dynamics are efficiently simulable by classical algorithms that track local information, even when conventional complexity measures such as the entanglement and magic are high. Here, we introduce a novel measure of complexity, the reactivity, to capture this new method of classical attack. Unlike conventional complexity measures, the reactivity does not capture a property of a quantum state or operator in isolation, but rather a quantum experiment as a whole. We provide numerical and rigorous evidence that quantum experiments with low reactivity are simple by a host of measures: they are efficient to classically simulate, learn, and fast-forward. This motivates the search for quantum experiments with high reactivity, which may evade these simplistic features. To this end, we introduce easily implementable experimental protocols—dubbed Pauli path spectroscopy—that allow one to efficiently measure the reactivity of any quantum experiment of interest. Our protocols are applicable even when the experiment itself is beyond the reach of classical simulation.

We propose a supersymmetric localization formula for the local perturbative contribution to the M-theory path integral, reducing it to an integral over equivariant flux data. Relative equivariant extensions of the eleven-dimensional Chern–Simons couplings determine the localized action, while for M2-brane backgrounds a tangent-cotangent character computes the one-loop determinant. This gives the first closed form expression for the complete perturbative ABJM partition function at general squashing and chemical potentials, and new analytic results for the ABJM topologically twisted index describing black holes. Applied to the non-toric $V^{5,2}$ theory, the same prescription yields a closed analytic Airy constant previously known only numerically. Our formulas reproduce all available independent field theory results, and provide analytic predictions at general parameters where no field theory answer is currently known. We derive an all-genus result for the Type IIA expansion which is an equivariant form of the usual topological string constant map result, and also extract integrated correlators.

We construct and study a “Cardy random matrix model”: a random matrix theory whose only input, in a maximal-ignorance prescription, is the constraint of $\mathbb{S}$-modular invariance. We regularize this constraint by coarse-graining over energy windows of fixed width, and obtain a potential for a single random matrix whose eigenvalues play the role of the scaling dimensions of primaries in a 2d CFT. The potential drives the coarse-grained density of states to the Cardy profile above a gap at the black hole threshold. We perform Monte Carlo simulations to confirm this behavior and find good agreement for the coarse-grained density of states, while at the same time revealing GUE statistics for nearby eigenvalues. We identify the scaling limit in which these phenomena emerge. In this limit, the model realizes a hierarchy of scales: at the macroscopic scale given by the window size, the occupations are frozen and the bootstrap constraint rigidly fixes the spectrum to the Cardy profile, while at the mesoscopic scale (inside a window) the Vandermonde repulsion rearranges the eigenvalues as in a random matrix theory. It is only at the microscopic scale of the mean level spacing that the individual levels are resolved. Accordingly, our random matrix model displays an effective Thouless time, set by the inverse energy width of the coarse-graining window. Our model provides a first step towards solving the matrix/tensor model dual to 3D quantum gravity on a computer.

We study massive spin-$1/2$ Boltzmann particles in global thermodynamic equilibrium with rotation and acceleration, consistently including quantum corrections up to order $\mathcal{O}(\hbar^2)$. For such a system, the fluid velocity becomes an independent thermodynamic variable and fundamental thermodynamic relations have to be extended. Employing the Wigner-function formalism, we show that the standard mass-shell condition $k^2 = m^2$ is modified at order $\mathcal{O}(\hbar^2)$ by contributions quadratic in the thermal vorticity. Incorporating this modified mass-shell constraint, we derive the (net) particle-number current, energy-momentum tensor, spin-current tensor, and associated thermodynamic quantities in the kinetic, canonical, and de Groot–van Leeuwen–van Weert (GLW) pseudo-gauges. We explicitly demonstrate that, while global quantities, like the total particle number or total energy, are independent of the choice of pseudo-gauge, local quantities, like the particle-number density or the energy density, are pseudo-gauge dependent. We then examine the thermodynamic relations in each pseudo-gauge and demonstrate that thermodynamic consistency requires that the thermodynamic Maxwell relations are satisfied. We find that these relations hold in the kinetic-theory pseudo-gauge, whereas they are in general violated in the canonical and GLW pseudo-gauges. These findings suggest a preference for using the kinetic-theory pseudo-gauge in applications such as spin hydrodynamics.