Papers

We initiate a systematic cosmological investigation of an axio-dilaton system governed by a curved field-space metric as generically motivated by supergravity and string compactifications. The scalar sector consists of a light scalar dilaton field evolving along an asymptotically exponential potential and a pseudoscalar field spanning an essentially flat direction, kinetically coupled through an exponential field-space metric. Deviations from the asymptotic regime are incorporated by introducing a generalised Albrecht-Skordis potential containing a polynomial factor. Utilising a dynamical systems approach alongside numerical evolution and Bayesian inference, we constrain the model using Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO) and Planck 2018 distance-prior data. We identify a parameter degeneracy indicating that steeper potentials demand stronger field-space kinetic couplings to sustain late-time cosmic acceleration. Finally, a joint likelihood analysis reveals that while the model successfully accounts for dark energy dynamics, it is only slightly statistically favoured over $\Lambda$CDM by current observations.

In this letter, we investigate the interaction between stationary point-like external sources within the framework of Pseudo-Quantum Electrodynamics (PQED). Besides ordinary electric charges, we consider configurations involving Dirac points and generalized topological sources. For the configurations analyzed, we compute the corresponding interaction energies, forces, torques, and electromagnetic field configurations. Furthermore, we compare the results obtained in PQED with those arising in ordinary planar Maxwell electrodynamics, showing that the nonlocal character of PQED gives rise to physical effects with no counterpart in the conventional local planar theory. In particular, our results show that topological sources induce intrinsically anisotropic and non-central interactions, leading to the emergence of nontrivial torques between the interacting objects. The directional character of these interactions suggests possible applications in the effective description of topological defects and anisotropic phenomena in planar condensed matter systems.

To elucidate the meaning of holographic entropy inequalities (beyond subadditivity) which characterize the entanglement structure of geometric states in holography, arXiv:2309.06296 proposed the "tripartite form" for these inequalities, consisting of tripartite information and conditional tripartite information terms with unit coefficients. While this provides a compact and useful packaging of the inequalities, it is not a priori guaranteed that all inequalities can be recast in this form. Here we conjecture that they can, and present substantial evidence, by proving that the two known infinite families of holographic entropy inequalities found in arXiv:2309.15145 can indeed be written in the tripartite form. This is significant because such recasting is particularly nontrivial for these families. Apart from providing the explicit tripartite form expressions for every member of these two infinite families, we detail how we arrived at them, in the process deriving several useful identities which may serve as stepping stones to formulate further repackaging of the corresponding information quantities. We also illustrate the power of the tripartite form by proving a number of structural properties satisfied by any holographic entropy inequality.

We present a nonparametric determination of spatial curvature using only late-time geometrical probes. Under a Gaussian Process smoothness prior, we jointly constrain the dimensionless expansion history and $\Omega_K$, combining three Type Ia Supernovae (SNeIa) samples with either DESI DR2 line-of-sight baryon acoustic oscillations (BAO) or cosmic chronometers (CC) data. From our baseline SNeIa+BAO analyses we find $\Omega_K=0.219^{+0.110}_{-0.111}$, $\Omega_K=0.330^{+0.098}_{-0.150}$ and $\Omega_K=0.260^{+0.124}_{-0.127}$ for the PantheonPlus, DES Dovekie and Union3 SNeIa samples respectively. These nonparametric results mildly favour an open Universe, supporting recent hints in this direction, and improve on the sensitivity of a previous application of the method by up to a factor of $\sim 2.5$. We find consistent constraints combining SNeIa and CC, whereas restricting SNeIa data to the redshift range covered by BAO somewhat weakens the constraints and shifts the PantheonPlus central value to $\Omega_K<0$. Our results depend only on late-time relative distances and expansion rates, making them insensitive to the absolute distance scale calibration, while relying neither on Cosmic Microwave Background data nor on a parametric dark energy model.

Non-thermal cosmological histories rest on the assumption that scalars displaced during inflation undergo coherent oscillations, dominate the energy density of the universe before Big Bang Nucleosynthesis, and decay perturbatively through gravitationally suppressed interactions. In addition, usually a single dark matter component is assumed. This early matter-dominated era is the basis for the usual predictions of non-thermal WIMP production, axion dark matter, entropy generation, and dark radiation. This paper examines whether this picture is dynamically robust against non-perturbative decay of the modulus condensate. In this work, we study non-perturbative particle production from oscillating moduli using the effective field theory appropriate to $G_2$ compactifications. We find that non-perturbative production of Wino-like fermions is strongly suppressed in the relevant parameter regime. In contrast, a modulus-dependent axion kinetic term admits narrow instability bands with growth rates that can exceed the Hubble rate. A linear Floquet analysis alone, however, cannot determine whether these bands significantly deplete the modulus condensate, since cosmic expansion, backreaction, rescattering, and higher-order operators in the effective theory can become important. As a result, the conventional modulus-dominated cosmology remains robust against Wino and gauge-field preheating, while the axion channel provides a potentially important modification that requires nonlinear study. If sufficiently efficient, axion production can alter the division of dark matter between Winos and axions and enhance the dark-radiation abundance.

Vector fields with a chiral, parity-odd coupling to a pseudoscalar field are known to undergo resonant amplification. In this work, we study this phenomenon in the context of cosmological gravitational particle production during early-universe inflation. We consider a massive vector (dark photon) field with a parity-odd coupling to the inflaton. There are two regimes of production, delineated by the relative size of the coupling and the dark photon mass, arising from a tachyonic instability, and a parametric resonance, respectively. As a result of the coupling, the transverse modes, subdominant in both the minimally and nonminimally coupled theories, can dominate the total late-time abundance. The viable parameter space for dark-photon dark matter is thus widened. Furthermore, in the tachyonic case, the production is dominated by a single helicity mode, leading to a population of chiral dark photons that can lead to potential parity-violating observational signatures. We further explore the dependence of the production on the reheating history, and find that information about reheating is encoded in the number density spectrum.

Matrix elements of simple operators are central to thermalization in chaotic quantum many-body systems. Their moments are often described statistically through the Eigenstate Thermalization Hypothesis. In this paper, we study a more refined characterization of these matrix elements: the eigenspectrum of simple operators once projected to microcanonical energy windows. The spectrum encodes all moments of the matrix elements at once, and is particularly relevant when the spectrum of the Hamiltonian is degenerate. Assuming that the eigenbasis of the simple operator is Haar-randomly oriented with respect to that of the Hamiltonian, we prove that the spectrum of an operator projected to a small microcanonical window obeys Gaussian random matrix statistics. We do this directly by studying the probability distribution inherited from the random orientation, as well as using tools from Free Probability Theory. We discuss the implications for BPS chaos and more generally for eigenstate thermalization.

We study linear gravitational modes, sourced far-zone fields, and quadratic energy balance in a four-parameter tetrad theory of gravity. The theory contains three parity-even torsion invariants and a parity-odd coupling $v^\mu a_\mu$, where $v_\mu$ and $a_\mu$ are the vector and axial torsion components. Linearizing around Minkowski spacetime and applying a scalar–vector–tensor decomposition, we find two tensor, two scalar, and four vector degrees of freedom in the generic nondegenerate parity-violating region. The tensor and scalar modes propagate at the speed of light, while the two vector branches have coupling-dependent propagation speeds. We derive their kinetic eigenvalues, characteristic speeds, and flux normalizations. An exact trace identity shows that the vector Hamiltonian is not positive definite in the generic branch, even when the kinetic eigenvalues are positive and the propagation speeds are real. We also derive the response to a general compact canonical source and obtain explicit source-to-amplitude relations for all eight linear polarizations. The field $V_\mu=\partial^\nu B_{\nu\mu}$ is used to illustrate intrinsic-spin multipoles. {We further prove that the quadratic Noether current equals the second-order Møller current for the chosen first-derivative tetrad Lagrangian and derive the corresponding mode-resolved energy and momentum fluxes.} The vector contribution remains a formal signed response because of the unbounded Hamiltonian. The stationary limit reproduces the results of Ref.~\cite{ShirafujiNashed1997}, and a representative parameter scan illustrates vector-mode splitting and kinetic degeneracy.

We construct a new family of exact spinning black hole solutions in five-dimensional General Relativity with a negative cosmological constant, which are dual to strongly coupled spinning plasma balls on four-dimensional Minkowski spacetime. In analogy with the recent discovery of such black solutions in four bulk dimensions, the boundary Lorentz factor acts as a new coordinate in the bulk, giving rise to a new UV region that, in our case, is locally a three-dimensional de Sitter spacetime times the real line. The dual energy-momentum tensor in this region describes a conformal anisotropic fluid that satisfies the weak and strong energy conditions.

In this work, we develop a generalized Hamiltonian formalism for spatially nonlocal field theories whose Lagrangian densities depend explicitly on both the local field and its spatially reflected counterpart. Starting from a generalized variational principle, we derive generalized Euler-Lagrange equations and introduce a generalized functional derivative that consistently accounts for reflected-field contributions. The proposed formalism is applied to three spatially nonlocal nonlinear Schrödinger equations. For the Ablowitz-Musslimani equation, we construct, to the best of our knowledge, the first standard Lagrangian density formulated directly in terms of the complex fields and derive its complete Hamiltonian formulation. The same framework is subsequently applied to the two Lagrangian nonlocal nonlinear Schrödinger equations introduced by Velasco-Juan and Fujioka, yielding consistent Hamiltonian formulations that reproduce the corresponding generalized Euler-Lagrange equations. These results establish a unified Hamiltonian framework for a broad class of spatially nonlocal nonlinear field theories.

The recent observation of the high-energy nuclear recoil event LZ230616 with a recoil energy around 248 keV provides an interesting possibility to probe inelastic doublet dark matter (iDM). However, the electroweak doublet DM scenarios face strong constraints from solar DM capture for DM masses around the TeV scale which give rise to correct thermal relic density. In this work, we revive the inelastic doublet DM (iDM) scenario via type-II seesaw. In particular, we consider an inert lepton doublet (ILD) DM. While the minimal ILD scenario gives the correct relic abundance around the TeV scale, it is strongly constrained by direct detection and solar DM capture. In the type-II seesaw, the presence of the scalar triplet generates the required mass splitting and provides additional annihilation channels, allowing the correct relic abundance for much larger DM masses. The larger DM mass also helps evade the solar capture and indirect detection constraints. Additionally, the scalar triplet gives sub-eV neutrino masses required by the oscillation data.

We investigate the weak and strong gravitational lensing of a dyonic black hole in Kalb-Ramond gravity. After fixing the asymptotic normalization, we distinguish the effective charge governing the local null trajectories from the global angular identification associated with Lorentz-symmetry breaking. In the weak-deflection regime, we evaluate the Gaussian curvature explicitly and apply the Gauss-Bonnet theorem with a perturbed ray boundary, recovering the complete second order mass contribution. Independent calculations based on the orbit equation, the turning point integral, and Fermat's principle reproduce the same bending angle. In the strong-deflection regime, Tsukamoto's method yields closed expressions for both strong-deflection coefficients, with exact charge dependence. We derive finite-distance lens equations and the associated image positions, magnifications, flux ratios, and differential arrival times, retaining the physical winding condition. Shadow sizes inferred from observations of Sgr~A$^*$ and M87$^*$ yield conditional charge bounds, complemented by an estimate from S2 precession. We further construct combinations of strong-lensing observables that separate the effective charge from the conical parameter within the model: angular separation and relative brightness remove the explicit winding dependence, while a timing ratio incorporating an independent distance estimate isolates the conical deformation.

Heating matter can restore symmetries spontaneously broken at low temperature. The axial $U(1)$ symmetry of quantum chromodynamics (QCD) is different: it is present in the classical theory with massless quarks but is broken upon quantization by the axial anomaly. The anomaly persists at every temperature, yet its observable effects can weaken. Can hot matter nevertheless behave as though this symmetry were restored at long distances? Whether such effective axial $U(1)$ restoration occurs depends on how microscopic quark and gluon dynamics governs the strength and spatial range of axial breaking. This review brings together theoretical developments and first-principles lattice QCD calculations. We examine how gluon-field topology shapes the low-lying Dirac modes and their correlations, how these modes contribute to axial breaking at different spatial scales, and what this implies for the order and critical behavior of the chiral phase transition as quark masses approach zero.

Brane tilings are bipartite graphs on a 2-torus that encode the Lagrangians of 4d N=1 supersymmetric gauge theories arising on D3-branes probing toric Calabi-Yau 3-folds. Among these bipartite graphs, only those that satisfy geometric consistency conditions correspond to well-behaved quantum field theories. We train a convolutional neural network (CNN) to distinguish geometrically consistent from inconsistent brane tilings directly from their Kasteleyn matrices. We study a family of 4d N=1 theories obtained by adding diagonal edges to the hexagonal faces of the brane tiling for the abelian orbifold C^3/Z_3 x Z_3, and find that the CNN identifies geometric inconsistency with high accuracy. For inconsistent brane tilings that can be rendered consistent by Higgsing a single bifundamental chiral field, we show that gradient-based saliency analysis can be used to localize the responsible chiral fields with accuracy well above a matched random baseline. These results demonstrate that explainable AI (XAI) can be used to identify local defects responsible for inconsistencies in supersymmetric gauge theories.

We use bosonic tensor networks to connect the lattice sine-Gordon model in the Hamiltonian formulation quantitatively to its continuum theory. Matching the lattice vertex operator to its conformal normalization at the free-boson ultraviolet fixed point yields the exact relation between the bare lattice coupling and the renormalized continuum mass parameter. The soliton mass then approaches Zamolodchikov's exact continuum prediction throughout the studied parameter range, without adjustable parameters. Using uniform matrix product states and a quasiparticle ansatz, we also recover the relativistic soliton dispersion and the two lightest breather masses at the percent level. We simulate real-time collisions of Gaussian soliton-antisoliton wave packets near a reflectionless point and extract the Wigner spatial displacement. We compare this displacement with the exact continuum prediction obtained from the momentum derivative of the transmission phase, recovering its characteristic rapidity dependence. Our bosonic simulations provide a foundation for nonintegrable extensions, offer lessons for renormalization in other Hamiltonian lattice field theories, including gauge theories, and provide benchmarks for continuous-variable quantum simulations.

Static, asymptotically flat, non-Schwarzschild black holes in four-dimensional Einstein–Weyl gravity have previously been constructed by numerical shooting, while the local field equations admit horizon and asymptotic expansions to all orders. We give a computer assisted existence proof for a non-Schwarzschild solution whose dimensionless horizon radius is one in units of the massive spin-two scale, with parameters close to the previously reported numerical branch. The exterior is divided into a convergent horizon series domain, a compact core enclosed by a parameter dependent Taylor model with directed rounding, and an infinite asymptotic domain treated as a centered stable manifold fixed point problem. The resulting five-dimensional matching map between the core and tail is continuous on a rigorously specified box. After exact rational preconditioning, the signs on opposite faces satisfy the hypotheses of the Poincaré–Miranda theorem and therefore certify a matching zero. The solution has a regular nondegenerate horizon, no additional exterior horizon, vanishing Ricci scalar, and nonvanishing Ricci tensor. The proof establishes existence, but not uniqueness of the matching zero.

We construct a maximally supersymmetric Type IIB background in signature $(5,5)$ on the real ten-manifold underlying complex $\mathrm{AdS}_5$. The spacetime is diffeomorphic to $T^*S^5$ and carries the invariant metric $G=\mathrm i(\bar q-q)$, where $q$ is the holomorphic constant-curvature metric. The real five-form $F_5=(4\mathrm i/L)(\Omega-\bar\Omega)$, built from its normalized volume form, is self-dual, and its stress tensor supports this scalar-flat, non-Einstein metric. We derive these fields from the most general $\mathrm{SL}(4,\mathbb C)$-invariant metric and five-form ansatz: self-duality and the Einstein equation fix their phases up to the overall scale, orientation, and flux sign. The fields obey the reality conditions of the untwisted $\mathrm{IIB}_5$ theory. The holomorphic coframe makes the supercovariant curvature cancellation explicit, and flat transport gives thirty-two global real Killing spinors. Their Killing superalgebra is the factor-exchanging real form of $\mathfrak{psl}(4|4,\mathbb C)$, and we identify the corresponding supercoset.

In this paper, we provide a systematic construction of quantum modules associated with coadjoint orbits of asymptotic symmetry groups through the path integral quantization at one-loop order. In particular, for the orbits with Hamiltonians unbounded from below, we show that an appropriate choice of integration contour defines a convergent Euclidean half-line path integral. The reference state associate with the orbit is determined by the path integral of the geometric action on the corresponding coadjoint orbit. The coadjoint module is therefore spanned by the reference state and its descendants. We apply this formalism to the Virasoro and BMS$_3$ groups and derive the coadjoint modules corresponding to all constant orbits. We also compute the characters of all constant Virasoro and BMS$_3$ coadjoint orbits by counting the states within the modules, and the results agree with the corresponding computations from the path integral of the geometric action with a periodic Euclidean direction.

The DeWitt boundary condition can be implemented in the Lorentzian path integral of minisuperspace quantum cosmology by summing only over non-singular paths. In this paper, we present a general definition of the resulting DeWitt kernels, along with specific rules for their construction, and evaluate them rigorously. The lapse integral over the positive half-line yields the Dirichlet Green function of the Wheeler–DeWitt operator, whereas the integral over the whole real line yields the Dirichlet group-averaging kernel; both vanish when either endpoint lies at the singularity. Since the minisuperspace actions are at most quadratic, all lapse integrals are performed in closed form without saddle-point approximations. We obtain the kernels for the closed universe without cosmological constant, for the flat de Sitter universe, and, in terms of Airy functions, for the closed and open de Sitter universes. Throughout, the DeWitt condition is imposed as the boundary condition at the singularity, which selects a self-adjoint constraint operator on the half-line and fixes the kernels uniquely, including their normalization.

In vacuum anti-de Sitter (AdS) space, the geometry admits a perfect tessellation by a geodesic network. This tessellation characterizes the background exactly, and a partial entanglement entropy (PEE) tensor-network toy model of AdS/CFT can be defined on it. It has so far been unclear whether this construction can be extended beyond vacuum AdS. In this paper we take the first step in this direction. We show that the exterior region of the Schwarzschild black hole and its Einstein–Rosen bridge are perfectly tessellated by a specific geodesic gas emitted from the boundary, so that Crofton reconstruction holds in these regions. We then prove that such a geodesic tessellation and the Crofton reconstruction it defines extend to more generic Riemannian manifolds. This allows us to construct a PEE tensor-network model of holographic duality on more generic geometric backgrounds. In the case of the PEE tensor-network model for the Schwarzschild background, we can concretely realize the Bekenstein–Hawking entropy, the Ryu–Takayanagi formula and the ER=EPR proposal. Our approach opens a new route towards holographic toy models beyond AdS/CFT.

We investigate the stability and localization properties of Minkowski, de Sitter (dS), and anti-de Sitter (AdS) thick branes generated by a complex scalar field $\Phi$. The scalar self-interaction potential contains a temperature parameter $a$. As $a$ approaches its critical value, the imaginary part of $\Phi$ becomes double-kinked and the energy density splits into two peaks, indicating the formation of two sub-branes. The analysis of linear scalar, vector, and tensor perturbations shows no signs of instability in the scalar and vector sectors, while the factorization of the tensor perturbation equation excludes tachyonic tensor modes. The graviton zero mode is localized on the Minkowski and dS branes but is not normalizable on the AdS brane. We further study a real test scalar field $\Psi$ with a coupling function $F(R)$ between its kinetic term and the spacetime curvature. The scalar zero mode can always be localized on the Minkowski and dS branes, with a continuous gapless spectrum of scalar Kaluza–Klein (KK) modes. Massive scalar resonances emerge near the critical value of $a$ for suitable values of $\beta$. Increasing $\beta$ produces more resonances and prolongs the lifetimes of the lower resonances, while their time evolution exhibits the characteristic decay of metastable modes. For the AdS brane, the scalar zero mode is also localized, whereas the divergent effective potential at the boundaries traps the massive scalar KK modes as bound states, yielding a discrete mass spectrum.

Recent work has constructed Abelian Chern-Simons theories as categorical TQFTs, allowing us to naturally incorporate categorical defects and construct defect extensions of Abelian Chern-Simons TQFTs. We first identify the Turaev-Viro realizations of Abelian Chern-Simons theory in the center and doubled pointed modular cases, clarifying the distinction between single bulk realizations and canonical doubled ones. Then we obtain Turaev-Viro partition functions in terms of Reidemeister-torsion densities. Alternatively, the Alterfold construction supplies the associated topological boundaries, domain walls, and condensation sectors, establishing an explicit Alterfold/Chern-Simons dictionary. We show that the finite quadratic module is the invariant controlling the bulk theory, its topological symmetries, orientation-reversal invariance, and defects. We further show that multicomponent Abelian BF theory arises as the extended TQFT of an off-diagonal Abelian Chern-Simons theory, placing it naturally within the same extended framework. Finally, we demonstrate that recently proposed Abelian Chern-Simons dualities do not define a genuine TQFT duality. These results provide a concrete model for defects in Abelian topological orders and suggest a route toward the non-Abelian case.

The bit thread formulation provides a geometric description of holographic entanglement entropy, while partial entanglement entropy (PEE) and PEE threads resolve this structure with respect to individual boundary points. Motivated by the fact that PEE thread flows can be superposed to reconstruct conventional bit thread flows, we introduce a differential form description of PEE thread flow. For an interval in the vacuum AdS$_3$/CFT$_2$ setup, we show that the flux of the resulting form reproduces the known entanglement contour, providing a consistency check of the proposed description. We then investigate whether the PEE form can be related, possibly up to an exact form improvement, to a current constructed from the covariant phase space (CPS) formalism. As a first test, we consider exact Killing vectors in Rindler-AdS$_3$. The Rindler parameter $a$ parametrizes a one-parameter family of backgrounds. At each value of $a$, the Killing vector of the corresponding background is substituted into the Iyer-Wald surface charge form, and the full $a$-dependence of the resulting form is retained. We define a finite candidate current by integrating this surface charge form over $a$. For the reflection-symmetric PEE flow sourced at the central boundary point $r_0=0$, we find that no choice of the Killing parameters reproduces both components of the known PEE flow after transforming to Poincaré-AdS$_3$. This result shows that the direct Killing vector CPS construction considered here is not sufficient to reproduce the central PEE flow. Possible extensions include an exact form improvement, a different CPS current, or a more general choice of generator.

Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.

In this article, I will define the Chern-Simons invariant of a gauge connection over a three-manifold and explain some of the things that are special about it, in particular its role in understanding the quantum Hall effect, which is an important effect in condensed matter physics, and its generalization, the fractional quantum Hall effect. (The article is based on a lecture at a conference celebrating the 75th birthday of James Simons, held at the CUNY Graduate Center in 2013. It will appear in the Bulletin of the American Math Society.

A large catalog of asymptotically free and anomaly-free SU(N) chiral gauge theories that admit a large-N limit was constructed by Eichten, Kang, and Koh. Here we compute the global structure of their symmetry groups and tabulate the 't Hooft anomalies of the faithful symmetries, including those that are visible only in backgrounds carrying fractional flux. Most theories in the catalog contain fundamentally charged matter and support no genuine one-form electric center symmetry. However, fractional fluxes still arise from the faithful quotient and contribute to the anomaly in the same way as a two-form background for a one-form symmetry. The anomalies are computed using two methods, first with the descent procedure, and second by placing the theory on a four-torus, which supports twisted fluxes for background gauge fields. We discuss a selection of candidate IR behaviors and present a general discussion of how matching the anomalies associated with fractional flux can constrain infrared descriptions beyond the imposition of ordinary zero-form anomaly matching at the level of triangle diagrams. Based on large-N reasoning, we formulate a new proposal for the IR behavior of a pair of models, consistent with the ordinary zero-form 't Hooft anomaly matching conditions. In this case the matching condition involving fractional flux is satisfied automatically as a consequence of ordinary matching.

We consider $V_{g,n}(\{b_i\})$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus $g$ with $n$ geodesic boundaries of lengths $b_i$, $(i=1,...,n)$, and various ${ N}{\geq}1$ supersymmetric generalizations of them, using a framework within which they are specializations of a larger family of quantities naturally governed by the integrable KdV hierarchy. An exact boundary-addition identity is derived that directly relates $V_{g,n+1}(\{b_1,b_2,...,b_n,b\})$, for any $b$, to the corresponding $n$-boundary KdV data underlying $V_{g,n}(\{b_1,b_2,...,b_n\})$. For ordinary Weil-Petersson volumes, expansion about the special removable-cone value $b=2\pi i$ reproduces three known results of Do and Norbury, organizing them as the first levels of a complete hierarchy. The higher levels are naturally built from additional KdV data, which we interpret geometrically in intersection theory as a tower of $\kappa$-decorated volumes. Several other recursive relations in the literature are illuminated by the identity, and various new ones are derived. The cases with ${ N}=1,2$ and (small) ${N}=4$ supersymmetry are also covered by the identity, and we exhibit some of the striking special features and results arising in each case. Among many applications presented, we use the identity to uncover the intersection theory descriptions of ${N}=2$ and small ${ N}=4$ Weil-Petersson volumes.

Motivated by the $2.6\sigma$ high-energy recoil event recently reported by the LUX-ZEPLIN (LZ) Collaboration, we consider an endothermic $Z^\prime$-portal Majorana dark matter framework and discuss the complementarity between the LZ event and LHC searches for a $Z^\prime$ resonance. As a concrete realization, we consider a gauged U(1) ${B-L}$ extension of the Standard Model. The phenomenology of the framework is essentially controlled by two free parameters: the U(1) ${B-L}$ gauge coupling $g_{BL}$ and the $Z^\prime$ boson mass $m_{Z^\prime}$. For a fixed $m_{Z^\prime}$, the observed dark matter abundance requires the dark matter mass to be near the $Z^\prime$ resonance, $m_{\rm DM} \sim m_{Z^\prime}/2$, and sets a lower bound on $g_{BL}$. Complementarily, LHC searches for a $Z^\prime$ resonance set an upper bound on $g_{BL}$. The parameter space allowed by the dark matter abundance and LHC constraints can account for the recent LZ event. The synergy between future $Z^\prime$ resonance searches at the High-Luminosity LHC and the LZ experiment may provide a test of this framework.

We use a point-particle effective field theory to study the superradiant instability rates of an ultralight massive vector around a slowly rotating black hole. Earlier effective-theory treatments reported an apparent $O(1)$ discrepancy with the rates obtained by solving the Proca equation on a fixed black-hole background, e.g. for the mode with $j=1$ and $\ell=2$. We show that there is in fact no discrepancy: once the leading-order states in the degenerate $\{\ell=0,\ell=2\}$ subspace are correctly identified, the effective theory (implemented here with the graviton integrated out exactly, and expanded in $\alpha$ only afterwards) reproduces all of the $j=1$ Proca instability rates exactly, and it does so without ever invoking the FKKS ansatz on which the full-theory calculation rests. Since it never relies on separability, the same approach applies, at least in principle, to rotating backgrounds and bodies that lack the hidden symmetries underlying that ansatz. The single ingredient beyond the far zone is a conservative worldline contact term, the static monopole response of the horizon in the parity-even $j=1$ Proca sector, which we fix by matching to the near zone. The same term shifts the fine-structure splitting of the bound states into exact agreement with the published Proca spectrum. In addition to providing a conceptually straightforward model of vector superradiance and resolving an apparent tension in the literature, we present this work to illustrate potential technical subtleties involving dissipative effects in point particle effective theories.

We study a zero temperature, degenerate, fermion gas with fermions of rest mass $m$, that only interacts with itself, gravitationally. We describe a self-consistent novel approach to the formation of a degenerate, quantum mechanical, star. In this approach, the fermions occupy the energy levels that are determined by the self consistent gravitational interactions, according to the Pauli exclusion principle. Then the size of the highest occupied level determines the radius of the star. In the Newtonian gravitational limit, the fermions feel a potential corresponding to a simple harmonic well that smoothly attaches in the exterior to the usual $1/r$ Newtonian gravitational potential. We find analytically, solutions for stars with any radius and mass, parametrized by $m$ and $N_s$, the total number of fermions. In the Newtonian limit, we easily find that we can construct a star that is more compact than the Buchdahl bound and indeed can even be smaller than the Schwarzschild radius. Clearly, such cases are outside of the purview of the Newtonian limit. Therefore we expand our analysis to fermions in the general relativistic context, interacting gravitationally with a metric. We consider the metric corresponding to the interior Schwarzschild solution smoothly connecting to the usual exterior Schwarzschild metric. Treating matter semi-classically, we recover the Buchdahl bound in a completely independent analysis. We briefly discuss classical stability of the Newtonian solution, and its relation to Newtonian polytropic fluids.