Papers

We develop a systematic, Whitham-based construction of perturbative/non-perturbative (P/NP) relations for one-dimensional quantum mechanical systems admitting a genus-one WKB period description, and derive a higher-genus formulation under explicit regularity assumptions. We select external deformations that preserve the independent quantum residues and lift them by varying the internal moduli so that the independent perturbative quantum periods remain fixed. The Riemann bilinear identity then determines the induced evolution of the non-perturbative periods through local residue pairings and the inverse period Jacobian. At genus one, this reduces to a relation between the flow of the non-perturbative quantum period and the energy derivative with respect to the perturbative action, providing a constructive connection between the Rayleigh-Schrödinger expansion and fluctuations around non-perturbative saddles. We recover known P/NP relations and derive extensions for explicitly coupling-dependent potentials, which we verify at the computed orders through independent perturbative and non-perturbative period calculations for quantum-corrected quartic and Jacobi elliptic examples.

In this paper, three formulations of spin-$1/2$ Second-Order Pseudo-Hermitian quantum field theorIES (SOPHIES) are built from scratch from parity eigenstates. Pseudo-Hermiticity allows the unconstrained fields to satisfy either Fermi–Dirac or Bose–Einstein statistics, while self-conjugate Majorana-like fields are only compatible with Fermi–Dirac. The set of independent four dimension renormalizable self-interactions of the three theories are identified, and the one-loop renormalization of the unconstrained fermionic and bosonic theories coupled to an abelian gauge boson and enhanced with a Pauli term and including self-interactions is studied, together with the one-loop renormalization of the only independent quartic self-interaction of self-conjugate fields. The analysis leads to a rich set of Renormalization Group Equations with deep connections to known theories, like the Dirac formalism and the Klein–Gordon scalar through the fixed points of the Pauli coupling.

We formulate an S-matrix bootstrap in an exactly flat half-space, where boundary reflection provides geometric infrared control for four-dimensional gravity. Under the channel positivity conditions, we obtain an infrared-finite positivity bound on local four-scalar Wilson coefficients that includes a finite gravitational correction of order $G_N$ and is derived from the full UV absorptive spectrum without specifying a UV theory, imposing a spectral ansatz, requiring weak coupling or expanding the spectrum perturbatively. At fixed dimensionless external state parameters, the coefficient of the leading gravitational correction is independent of the EFT scale and requires neither an arbitrary soft resolution scale nor a model-dependent UV scale. Gaussian wave-packet scattering localizes interactions within the flat region and directly probes bulk Wilson coefficients while exponentially suppressing sensitivity to the boundary. Long-range gravitons remain sensitive to the boundary and give a finite contribution. The smearing functional passes numerical positivity tests with general half-space absorptive kernels in both crossed channels. An explicit string example shows how boundary reflection suppresses the collective contribution of string resonances to the absorptive part of the amplitude, connecting infrared control of low-energy scattering to the UV spectrum of quantum gravity in the same dispersion relation. The framework opens a route to infrared-finite constraints on effective interactions across particle physics and gravity.

We apply large $N$ expansion techniques to derive kinetic equations for strongly coupled, far-from-equilibrium field theories with $O(N)$ symmetry. For large $N$ vector models, the quasi-classical approximation holds. Incorporating arbitrary momentum-dependent interactions, we show the dynamics obey the standard kinetic equation, with the scattering amplitude given by the retarded propagator of the auxiliary Hubbard-Stratonovich field. This has broad applications to systems like spin wave and Langmuir ion-acoustic turbulence. For large $N$ random coupling (SYK-like) models in $d$ dimensions, leading-order melon diagrams induce order-one propagator renormalization and finite spectral width. The corresponding kinetic equation, unlike those for standard weakly interacting systems, does not have a local-in-time collision integral. We find evidence for a stationary, scale-invariant infrared solution, revealing a potentially novel strong turbulence scaling exponent.

We study the tree-level fermion-photon effective vertex for on-shell particles in a relativistic environment undergoing rigid rotation at zero temperature. The rotational background breaks translational invariance in the transverse plane and introduces a preferred direction, leading to a distinct decomposition of the vertex into longitudinal and transverse structures with respect to the rotation axis. Using fermion and photon modes constructed in the rotating frame, we derive the corresponding selection rules and show that the energy and the longitudinal component of the momentum are conserved, whereas no independent transverse momentum-conservation condition arises. Instead, the transverse dependence is governed by radial integrals involving three Bessel functions, whose support constrains the magnitudes of the transverse momentum projections. The vertex can be organized in a circular basis for the transverse components and a Cartesian basis along the rotation axis, and expressed in terms of six Dirac structures. Their coefficients define 24 form-factor components associated with the photon-mode components, physical photon states, and spin-dependent structures induced by the rotating background. We also verify current conservation and gauge invariance of the resulting tree-level matrix element under the boundary conditions considered. These results provide the tree-level structure of the fermion-photon interaction in rotating relativistic matter and establish the basis for the study of radiative corrections in vortical backgrounds.

Gravity from entropy (GfE) identifies its Lagrangian with the geometric quantum relative entropy (GQRE) between the spacetime metric and a metric induced by matter and curvature, treating the metric itself as a quantum operator. We extend this construction to the Tsallis, Rényi, and Sharma-Mittal families, which we call gravity from generalized entropy (GfGE), and determine their common Einstein limit, weak-field spectra, auxiliary-field formulation, and horizon entropy. The entropy choice controls the leading higher-curvature terms and additional modes. We confirm that the linearized GfE spectrum contains a healthy scalar and a Planck-scale tachyonic spin-2 ghost. We identify the conditions that remove this ghost: curvature must enter through its scalar trace, or the entropy generator must be flat to quadratic order at the identity. The latter gives exact general relativity for Tsallis at $q=0$ and ghost-free $f(R,L_m)$ theories for Rényi and Sharma-Mittal. On shell, the auxiliary G-field is proportional to the tensor in Wald's entropy formula. For analytic entropy functions, horizons with a single curvature scale have an area term followed by constant and inverse-area corrections. We also extend the volume-constraint cosmological constant to the full family; its leading entropy dependence is set by the scalar mass. A finite set of entropy-function derivatives controls the leading weak-curvature departures from general relativity.

We study coherent states of neutrinos electroweakly interacting with rotating matter. We start with the Dirac equation for a massive neutrino propagating in background matter with a coordinate dependent effective potential. Then, we consider the limit of massless particles and the specific matter velocity profile. It allows us to reduce the neutrino Hamiltonian to the harmonic oscillator form. We find the exact solutions of the Dirac equation and construct the creation and annihilation operators. Using these results, we build the generalized coherent states of neutrinos. We provide the interpretation of these coherent states in terms of the classical physics. In particular, we demonstrate that the coherent states constructed approach plane waves in the limit of slow matter rotation. We also define the effective neutrino mass owing to the interaction of a massless neutrino with rotating matter. Then, we consider a special case of the generalized coherent states which are called the neutrino coherent states. The situation of the degenerate parameters of the system is also studied. Finally, we apply our results for astrophysical neutrinos propagating in dense matter of a rapidly rotating neutron star (NS). We calculate the effective neutrino masses for different neutrino energies for realistic parameters of NS.

This is my written Laudatio for Graeme Segal on receiving the Chern Medal at the 2026 International Congress of Mathematicians. I make some general remarks about Segal's qualities as a mathematician. Then I discuss the origins of his work on classifying spaces of categories and Gamma-spaces. In the last section I describe his axiom system for Wick-rotated quantum field theory and some of his subsequent work in the area. Of course, this is necessarily only a small slice of Segal's total research output.

Symmetries of a quantum field theory or a quantum lattice model are expected to be described not by a group but by a homotopy type, whose homotopy groups are the higher symmetry groups and whose Postnikov invariants encode 't Hooft anomalies. We propose a homotopy-theoretic definition of 't Hooft anomalies based on the structure of localized symmetries in the operator-algebraic approach. The input is a crossed precosheaf: a collection of groups attached to regions of space, equipped with pairings recording that the commutator of two transformations localized in two regions is localized in their intersection. To a crossed precosheaf and a finite family of regions we attach a pointed connected homotopy type, the Cech-Loday classifying space. As the family of regions ranges over finite covers of space, the classifying spaces form a pro-object in the homotopy category. There is a canonical map from the ordinary classifying space of the symmetry group to this pro-type. Composing this map with a group action gives an anomaly whose nontriviality obstructs gauging. In favorable cases, the Cech-Loday space is essentially independent of the cover. In such cases, the homotopy fiber of the canonical map is a candidate for the classifying space of the higher group of symmetries. We give examples of crossed precosheaves arising from gauge transformations in continuum field theory and from quantum cellular automata and finite-depth circuits. For quantum spin systems in one and two dimensions, our construction recovers the Else-Nayak index and its generalizations to two dimensions.

The memory-burden scenario of black hole evaporation proposes that Hawking emission may become increasingly suppressed as maintaining stored quantum information becomes dynamically costly. In this work, we revisit this scenario and investigate the conditions under which information retention can produce a genuine dynamical burden. We derive general scaling conditions for incremental memory accumulation at a fixed fractional mass loss and establish a conditional no-go result: entropy-suppressed, zero-mean deposits with subextensive integrated correlations cannot produce an order-one luminosity modification through unamplified accumulation and bounded feedback. We identify three essential requirements for dynamical memory: a record of the past must be written, retained, and coupled back to subsequent evaporation. We illustrate these requirements with concrete toy models that exhibit either a prolonged but finite black hole lifetime or an asymptotically approached finite-mass state (an effective remnant). We further distinguish kinetic-memory, thermodynamic-memory, and spectral-memory sub-categories of possible memory-burden mechanisms. In particular, we demonstrate that an independently evolving memory variable can generate evaporation-accretion hysteresis, such that a black hole returning to the same mass may possess a different retained memory and consequently a different luminosity. This history dependence may have implications for primordial black hole phenomenology. Finally, we briefly discuss the possibility of "merger rejuvenation", in which black hole mergers reorganize or reset the effective memory state.

Quantum M2-brane instantons are studied in eleven-dimensional Freund-Rubin backgrounds. The construction uses the identification of the Calabi-Yau cone over the Sasaki-Einstein manifold $\mathrm{SE}_7$ with the geometric branch of the abelian moduli space of the dual superconformal field theory. A class of BPS cycles in $\mathrm{SE}_7$ wrapped by M2-branes is identified as links of two-dimensional holomorphic cones whose coordinate rings contain BPS monopole operators. The algebraic structure and R-charge assignment on the moduli space further allow the computation of both the classical exponents and one-loop partition functions of the corresponding M2-brane instantons. Several three-dimensional superconformal field theories are analysed explicitly, and the relation to the corresponding localisation matrix models is discussed.

We construct giant graviton expansions of the thermal and $(-1)^F$-graded partition functions of $\mathcal{N}=4$ and $\mathcal{N}=1$ super Yang-Mills theories at zero 't Hooft coupling. These observables are generically non-BPS and do not admit a direct bulk interpretation in a supergravity regime. Instead, we exploit the corresponding self-dual theories, which arise as chiral zero-coupling limits and admit twistor string holographic duals. We apply a quiver generalization of Murthy's expansion motivated by twistor strings. Notably, we obtain expansions at both finite and infinite $N$. We reproduce the terms in these expansions from bulk closed string and D-brane sectors, identifying the nonperturbative corrections with D-instanton/anti-D-instanton pairs. At infinite $N$, resumming the D-instanton sectors reproduces the Hagedorn temperatures of the free gauge theories, providing a microscopic bulk origin for their Hagedorn singularities.

We derive the junction conditions for spherically symmetric thin shells in Lovelock and Quasi-topological gravities along two independent routes: from the distributional form of the field equations, and from the boundary term that makes the variational problem well-posed in the non-null case. The former method is ambiguous as it stands, since the equations contain products of Heaviside step functions with a Dirac delta. We show that the singular parts of the field equations are exact differentials in the jumping variables, so that the Vol'pert chain rule for functions of bounded variation fixes these singular combinations uniquely and no products of two deltas survive for a single shell, finding that both routes then agree. The same rule yields the null junction conditions, for which no boundary term is available in Quasi-topological gravities, together with the mass conservation law of the shell. These results clarify recent questions concerning the existence of thin shells in these theories. In particular, we show that previous claims that the junction conditions force the shell mass to vary with radius are incorrect and arise from treating a trapezoidal approximation to the relevant distributional products as exact. Our results also provide a basis for the recent analyses of mass inflation in these theories.

We study two-point event shapes in planar $\mathcal{N}=4$ super Yang–Mills, with source, sink and detectors given in terms of half-BPS scalars and their light transforms. Akin to local correlation functions, at order by order in perturbation theory, in the large charge limit, this event shape factorizes into the product of two octagons evaluated on the unit circle. Borrowing the octagon results, we study its behavior with respect to the coupling and the angle between the detectors.

We study the arithmetic structure of non-invertible duality defects in 4d $U(1)$ Maxwell theory. First, we recast the problem of realizing an elliptic $SL(2,\mathbb{Q})$ transformation as a duality defect in terms of complex multiplication for two-tori. The resulting classification includes well-studied cases in the literature, but extends to infinite Diophantine families of defects at a given gauge coupling. Second, we describe their worldvolume theories explicitly, with the Chern–Simons couplings determined by using continued fractions and tridiagonal continuant matrices. Third, we work out the fusion products of these defects, extracting the condensation defects and decoupled sectors both by lattice arithmetic and from the worldvolume descriptions. Finally, we illustrate our findings with the familiar $N$-ality defects (with $N=2,3$), but also give examples of infinite order.

Gravitational perturbations of rotating black holes in higher dimensions generally obey coupled partial differential equations. We show that scalar gravitational perturbations invariant under rotations of the transverse sphere of a singly spinning Myers-Perry black hole separate, despite the obstruction to a decoupled Teukolsky equation. Two commuting, second-order angular operators organise the three gauge-invariant curvature components into joint eigenfunctions. The physical radial problem is a $2\times2$ first-order system, equivalent to a single second-order equation. This gives a separation of the sector containing both the bar-mode and axisymmetric ultraspinning instabilities. Using only ordinary differential equations, we compute the bar-mode quasinormal spectrum in $d=5,6,7$ and find instability onsets at $a/r_+=0.90498$ and $0.83228$ in $d=6,7$. We also compute the growing axisymmetric modes and their onset rotations in $d=6,\ldots,9$. The construction shows how separability can survive the coupling between gravitational polarisations.

Stabilizer Rényi entropy quantifies magic relative to a complete Pauli frame. In settings such as helicity states of massless particles, unsynchronized qubit registers, energy eigenbases, and systems under superselection rules, the computational basis may be fixed while the transverse Pauli axes remain unspecified. The stabilizer Rényi entropy then depends on the choice of those axes. We define a phase-averaged stabilizer Rényi entropy by averaging the Pauli moments before taking the logarithm. It is exactly invariant under independent local rephasings. For pure states, it vanishes precisely when the state is a stabilizer state in every phase convention. For a broad class of sparse supports, it reduces to a closed-form function of the basis-state probabilities alone. Within this class, the ceiling for $n$ channels is $\ln[n^{3}/(6n-5)]$ for $n\geq3$ and $\ln\frac{7}{5}$ for two channels. We apply the invariant to tree-level gluon scattering at four and five points, where the helicity-basis phases are unspecified. It saturates the two- and three-channel ceilings: $\ln\frac{7}{5}$ at four points and $\ln\frac{27}{13}$ in $3\to2$ scattering. In same-helicity $2\to3$ scattering, it lies between a floor of $\ln\frac{8}{7}$ and a ceiling of $\ln\frac{184}{125}$, reached in the resolved soft limit and particular collinear limits, respectively. In every configuration studied, the invariant is independent of the fixed external colors.

Chiral topological order is incompatible with strictly two-dimensional local commuting-projector Hamiltonians on finite-dimensional tensor-product Hilbert spaces. Invertible subalgebras (ISAs) provide an alternative framework. We construct an ISA supporting chiral semions, together with its anti-semion commutant, on a square lattice with one qubit per edge. We give explicit non-Pauli generators for both algebras and prove that together they generate all local operators on the Hilbert space. Starting from the $\mathbb{Z}_4$ toric code, we condense the boson $e^2m^2$ and identify the semion and anti-semion algebras. We then decompose each $\mathbb{Z}_4$ qudit into two qubits and use a finite-depth circuit to disentangle one qubit per edge fixed by the condensation constraints. Pumping the semion ISA along the $z$ direction defines an explicit three-dimensional non-Clifford quantum cellular automaton (QCA). We show that pumping eight times is equivalent to a translation followed by a finite-depth quantum circuit with ancillary qubits. We also give an explicit finite-depth circuit relating this construction to the semion QCA previously obtained from topological quantum field theory. A similar condensation construction yields a $U(1)_4$ ISA on a square lattice. Together with the semion and earlier odd-prime ISAs, finite stacking realizes every pointed Witt class of bosonic Abelian anyon theories. Finally, we extend both constructions to all spatial dimensions $d=4k{-}2$, with one qubit or $\mathbb{Z}_4$ qudit on each $(2k{-}1)$-cell for the semion or $U(1)_4$ ISA, respectively.

Despite extensive work on BPS black holes in 4d flat space, there is no direct microstate counting from D-brane quantum mechanics in regimes described by Einstein gravity. We derive an exact formula counting BPS configurations of the D-brane system corresponding to black holes in $N=8$ supergravity obtained from type II strings on $T^6$. As part of the derivation, we relate the BPS equations to a solvable modified Calogero-Moser system. The result agrees with the prediction from the modified elliptic genus of the D1-D5 system, providing a highly nontrivial test of the string dualities relating the two descriptions. We emphasize that this quantum mechanical system is, as a model of quantum black holes, simpler than BFSS and propose some numerical tests to explore this.

Motivated by the 3d-3d correspondence, we introduce an index $\mathcal{I}_g^\phi$ for a mutation loop $\phi$ of a quiver and an integer $g \geq 0$. We prove its integrality $\mathcal{I}_g^\phi \in \mathbb{Z}$ under certain conditions, which extends the integrality conjecture of Gang–Kim–Yoon for $3$-manifolds to the broader framework of mutation loops in cluster algebras. Our index also has an interpretation as the genus-$g$ partition function of a $(1+1)$-dimensional TQFT. We provide explicit computations for mutation loops of period one. In particular, in the case of the generalized Kronecker quivers, we give an explicit formula expressing the generating function of the indices for all genera $g$ as a ratio of polynomials. Altogether, we provide a new insight to the interplay between the geometry of $3$-manifolds and cluster algebra.

We study the invariant rank-four deformed Hermitian–Yang–Mills equation associated with the chain $\mathcal{O}(1)\to\mathcal{O}(2)^{\oplus2}\to\mathcal{O}(3)$ over $\mathbb P^1$, with vertical weights $(4,2,0)$ and a fixed product Kähler class and phase. For arbitrary linear arrows $\psi=Bz$ and $\phi=(Az)^T$, smooth strictly calibrated reduced solutions exist exactly when $A$ is invertible and $z^TA^TBz$ is not identically zero. The same condition characterizes stability, semistability and polystability in the specified equivariant coherent category. The classification includes all eleven nonempty coefficient strata and both coincident and distinct divisor points on the rank-one lower boundary. The analytic proof retains the ordered, noncommuting middle equation. After constructing positive-parameter solutions, it rules out unbounded metric values by combining the source budgets with moving spectral tests; on the rank-one lower boundary, the divisor mass must also be retained. Global value, gradient and symbol estimates then give a smooth strictly calibrated endpoint on the original chain. No equivalence with full coherent or derived-category stability, uniqueness, or estimate uniform across changing chains is asserted.

We compute the one-loop gauge-field two-point functions analytically in scalar QED on dS$_{d+1}$ for general dimension and scalar mass, using the EAdS reformulation of the in-in formalism arXiv:2007.09993. The Dirichlet EAdS gauge field acquires a Schwinger-type mass, with its longitudinal mode supplied by a composite of charged scalars obeying opposite boundary conditions, while the Neumann mode remains protected by gauge invariance. In dS, the Dirichlet correction induces an anomalous dimension $\gamma_J$ for the boundary current and modifies the late-time falloff of the electric field. This bulk calculation reproduces the boundary multiplet-recombination result of arXiv:2509.18888. Summing over the in-in contour branches gives the retarded dS bubble kernel, making direct contact with the Bros-Moschella framework. We establish a spectral Cutkosky rule that expresses the discontinuity of this kernel across the principal-series cut in the Casimir plane in terms of a two-particle cut, with both internal scalar lines placed on shell. Although the full bubble coefficient involves a ${}_7F_6$ hypergeometric function, the cut collapses to a closed product of Gamma functions and determines the complete non-local part of the kernel through a dispersion relation. Analytic continuation of the same cut reproduces the complete one-loop result for $\gamma_J$. In the complex Casimir plane, the loop-corrected Dirichlet photon appears as a pole on the second sheet and is therefore naturally interpreted as a dS resonance, or quasinormal mode, whose frequency is shifted at one loop.

Gravitational tail-of-tail corrections arise when radiation scatters twice from the mass-monopole field of its source. In the multipolar effective field theory, one of the two-loop topologies contributing to this process involves genuinely coupled loop momenta, preventing its evaluation through nested one-loop integrations. After tensor reduction, this nonfactorizing structure leads to a particularly challenging family of scalar integrals with unbounded numerator powers as the multipole rank increases. We derive exact closed-form expressions for the entire relevant integer numerator domain, valid in generic dimension and accommodating Feynman, retarded, and advanced prescriptions through consistent analytic continuation. Near $d=3+\epsilon$, we also obtain explicit Laurent expansions through $O(\epsilon)$, retaining the subleading information needed in higher-order radiative calculations. While these expansions determine the dimensional poles, identifying their ultraviolet (UV) or infrared (IR) origin requires a separate analysis of momentum regions. We carry out this analysis throughout the integral domain and apply it directly to the coupled tail-of-tail emission diagram for arbitrary electric and magnetic multipoles. In this way, we independently determine the UV and IR residues, and explicitly verify that the complete infrared pole structure, including both double and simple poles, agrees with the exponentiation of the one-loop gravitational tail. The UV residues, calculated directly from hard-momentum regions, reproduce the established multipole anomalous dimensions when combined with the known contributions of the remaining diagrams.

We study the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors. The method expresses these asymptotics as a functional of an effective phase shift. We determine its two branches on either side of a quadratic stationary point and the transition profile joining them. The profile is expressed through parabolic-cylinder functions. Its connection to the high-temperature Gaussian $\beta$ ensemble fixes the finite normalization, in agreement with an independent Riemann–Hilbert analysis. We also show that the leading exponential asymptotics suffice to recover the Euler-scale prediction of generalized hydrodynamics for the dynamical structure factor of hard rods.

We study the imaginary part of the holographic timelike entanglement entropy (HTEE) in a charged asymptotically AdS$_5$ black-hole background whose dual field theory exhibits a critical point in the presence of a chemical potential $\mu$ and temperature $T$. Identifying the imaginary part of the HTEE with the imaginary part of the pseudoentropy, we derive an analytical expression for this quantity and investigate its behavior on the stable and unstable thermodynamic branches. We find that the imaginary HTEE vanishes in the uncharged limit and is induced entirely by a nonzero chemical potential, signaling the emergence of quantum coherence between the initial and final states. As the dimensionless ratio $\mu/T$ approaches its critical value, we obtain an inverse-square-root divergence in the derivative of the imaginary HTEE and extract the critical exponent $\theta_I = 1/2$ analytically. We further show that the same exponent governs the temperature response at fixed chemical potential. Our results establish the imaginary part of the HTEE as a non-local quantum-information probe of criticality in strongly coupled systems, and they imply that the initial and final states become maximally coherent at the critical point.

We quantize, in the homogeneous temporal gauge, both the electric and the magnetic Carrollian Yang-Mills theories with SU(N) gauge symmetry in the fundamental representation. We use the BRST method implemented in the path integral. We show that in the first case all the interaction vertices vanish, thus, giving a free theory. In the magnetic case, there are no loop contributions to the Green functions of the elementary fields –i.e., Green functions not involving composite operators– and the only connected parts of such Green functions with a dependence on the coupling constant are the tree level contributions to the three and four point functions of the field $\xi_i$. We also show that in the magnetic case the Green functions involving only Wilson loops are trivial and not so in the electric case.

The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity algebras. With $N=4(n+1)$, a tetracode character gives eight nonzero homogeneous components of dimension $t_n=8n+3+2^{4n}$. On a tip, a compatible grading has zero component of dimension $8n-5$ and eight nonzero components of dimension $1+2^{4n-3}$. The arithmetic behaves differently: for $n\geq2$, the lattice $D_N^+$ has no full-rank orthogonal frame of unscaled $A_2$ lattices. We exhibit failures of the Jacobi and Jordan identities and determine the derivations and full automorphism group of the ambient algebra above level one. We also give a Clifford-module proof, with the normalization fixed by root products, of the published realization of EP tips as special Vinberg $H$-algebras. This identifies a positive real form and yields explicit formulas for its cone, cubic, Cholesky coordinates and rational dual invariant. The cone is symmetric exactly at $n=1$. Its determinant-one hypersurface belongs to the known $L(8n,1,0)$ series, whose $r$- and $c$-maps give homogeneous scalar manifolds for supergravity theories with eight real supercharges.

We study collective charge excitations in pseudospin-1 triple-point semimetals within the random-phase approximation, considering both the linearised model with a flat-band and its quadratic-corrected counterpart. We analyse their density response, Drude weights, screening, plasmon dispersion and damping, particle-hole continua, and Friedel oscillations from the long-wavelength to the arbitrary-momentum regime. The quadratic correction renders the flat-band dispersive and endows it with a Fermi surface, thereby affecting the overall response. Comparisons with Weyl and Hopf semimetals reveal how bandstructure and quantum geometry jointly govern collective charge dynamics. While the Drude weights are determined by the Fermi surface and band-velocities, interband screening, plasmon dispersion, and Friedel oscillations reflect the quantum geometry of the eigenstates.

We study aspects of the Euclidean partition function of the $\frac{SL(2,\mathbb R)\times U(1)}{U(1)}$ gauged WZW model. The target space geometry is either a smooth horizonless geometry with a linear-dilaton asymptotic region, or the Horne–Horowitz black string, depending on which circles we unwind as the time-direction. We first study the worldsheet spectrum and obtain the character decomposition via the holonomy integrals. Next, we obtain the spacetime spectrum of the horizonless geometry by directly performing the unfolded modular integrals, and recover the Maldacena-Ooguri-Son spectrum in the ungauged limit. When the chirally charged three-dimensional black string is dimensionally reduced, the target space is instead a two-dimensional charged black hole. We study the near extremal regime of the black hole and black string. For the two dimensional black hole, we propose two candidate towers of states that produce the expected $\frac{3}{2}\log T$ of the AdS$_2$ throat from the worldsheet discrete series representation. These towers appear only below the temperature at which the full amplitude becomes divergent. We comment on the contribution of these states in the near-extremal limit of the full partition function.

Modifications of gravity beyond (vacuum) General Relativity have a subtle impact on the physics around black holes. Describing these effects across different observables is, however, a priori strongly model dependent. While effective descriptions of the geometry allow to efficiently capture deviations from benchmark predictions, they sometimes lack a clear passage towards (effective) new physics. Inspired by linear response theory, in this work I therefore propose a formalism that allows to calculate leading corrections of observables relative to the Schwarzschild black hole anywhere in space-time (outside of the horizon): the order of corrections is fixed through an eigenvalue $\mathcal{E}$ of the Einstein tensor, which is identified with an external energy momentum tensor that generates the deformation of the geometry. In this ways, $\mathcal{E}$ can be linked to effective physics models. Focusing on spherically symmetric and static black holes, I illustrate the approach at the hand of a number of observables in the vicinity of the horizon, such as characteristic quantities of particles moving around the black hole (e.g. the black hole shadow or the radius of the innermost stable circular orbit) or the spectrum of scalar quasi-normal modes. Reversing the logic, I argue that the knowledge of such observables provides non-trivial constraints on $\mathcal{E}$, which in turn grant insights into the effective physics in the vicinity of the black hole.