Papers

The unification of quantum mechanics and general relativity remains one of the major open problems of theoretical physics. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence provides a valuable theoretical framework for this effort via a holographic duality between a theory of quantum gravity in asymptotically AdS spacetime and a conformal quantum field theory on the lower-dimensional boundary. Here, we implement a toy model of this duality called the HaPPY code, a quantum error-correcting code in the form of a tensor network with hyperbolic entanglement patterns, on a trapped-ion quantum computer. We present the first experimental confirmation of the Faulkner-Lewkowycz-Maldacena formula in this model - a key test of the holographic correspondence. We then enrich it with non-stabilizerness, or magic, and observe entropic precursors expected of emergent gravity. Finally, we present and measure a code construction whose entropic behavior is reminiscent of a highly quantum wormhole. Our experiments illustrate how quantum computers can serve as testbeds for modeling the emergence of spacetime.

Extending heavy-baryon \(\chi\)PT to higher-spin resonances introduces unphysical lower-spin admixtures, leading to costly path-integral projections. To resolve this, we develop an on-shell implementation of the heavy-baryon expansion based on recoil-channel partial-wave eigenoperators. These eigenoperators separate the static mass dependence from recoil structures and assign chiral order directly in amplitude space. The resulting static–recoil factorization systematically generates non-redundant local operators for heavy-baryon sectors involving higher-spin resonances. Flavor structures and identical-particle constraints are imposed through a new linear-algebraic reduction that uses von Neumann alternating projections to extract the corresponding common physical subspace. Beyond this specific application, the framework can be broadly applied to general nonrelativistic effective field theories.

We present helicity amplitudes at three loops in the heavy-top quark effective theory of QCD for the scattering of a Higgs boson and three light partons with full-color dependence. To obtain these results, we use integration-by-parts identities implemented in the code Blade and evaluate the master integrals using canonical differential equations. We obtain compact analytic expressions in terms of generalized polylogarithms suitable for numerical evaluation. We observe that sub-leading color contributions at three loops are numerically as significant as leading-color terms. Our amplitudes are key ingredients for precision LHC phenomenology, for example in production cross sections involving a Higgs boson and a hadronic jet.

Quantum theory challenges the view that individual measurement outcomes are predefined and independent of the measurement context. Yet the quantum state itself – the catalogue of probabilities for all possible measurements – is usually assumed to be well defined. We argue that this assumption tacitly relies on measurements being performed relative to ideal, infinitely-resourceful reference frames. We show that, when measurements are made relative to non-ideal quantum reference frames, the probabilities themselves become indefinite: even in the limit of arbitrarily large number of runs, the relative frequencies may remain uncertain. The uncertainty is irreducible in a quantum-mechanical sense, as we show by proving a Bell-type theorem for relative frequencies. We further propose a quantum-optical implementation of these relational measurements based on pulsed homodyne detection. Our findings motivate an extension of the notion of the quantum state to regimes constrained by finite resources. We expect them to be especially relevant at the interface between quantum theory and general relativity, where the resources and information available in a bounded region of spacetime are fundamentally limited.

We show that the one loop effective action of type IIA and IIB string theories in ten dimensions have terms proportional to the dilaton times the ten dimensional Euler density, in apparent violation of the soft dilaton theorem. This can be traced to the existence of the zero modes of the world-sheet superconformal ghost fields and resolves a puzzle that arose recently in the analysis of black hole index when we compactify these theories on Calabi-Yau manifolds of non-zero Euler number.

Although symmetry-protected topological phases (SPTs) can be distinguished by their entanglement properties, it has been unclear how to extract this information directly from expectation values beyond the 1D case. Here, we close this gap and propose a pair of nonlocal order parameters that can detect and distinguish all bosonic SPTs in 2D protected by internal discrete, Abelian unitary symmetries. The desired topological invariants are extracted by these quantities by effectively simulating the SPT path integral on topologically non-trivial spacetime manifolds. Our order parameters are defined in terms of expectation values of partial symmetry and permutation operations acting on fixed numbers of replicas of the system in finite spatial regions. These expectation values correspond to symmetry-twisted versions of multipartite entanglement quantities known as multi-entropies. We show explicitly that our two order parameters detect symmetry-protected four-party and six-party entanglement, respectively, and we constrain possible "spurious" contributions. We analytically test our proposal in fixed-point lattice models. Our results suggest multipartite entanglement to be a defining feature of SPTs; indeed, we expect our methods to generalize to fermionic and higher-dimensional systems.

We study strong-to-weak spontaneous symmetry breaking (SWSSB) at finite temperature and its implications in holography. SWSSB is a novel critical phenomenon that arises only in mixed states. We demonstrate SWSSB with the BTZ black hole and show that, in the bulk, it is realized through wormhole geometries connecting the two copies in the thermofield-double construction. We point out that SWSSB can be recast as an emergence of global symmetries under ensemble averaging. We further examine the interplay between SWSSB and the swampland program, and propose a new swampland conjecture for quantum-gravity theories involving ensemble averages.

We prove sharp bounds on the moduli space excursion that is possible outside the event horizon of a spherically symmetric charged black hole. In regions where the black hole charge $Q (\phi)$ is no less than its asymptotic value, we prove that the total moduli space excursion is less than $\frac{\pi}{2\sqrt{k_N}}$ where $k_N$ is the rationalized Newton constant. We also show that the moduli space excursion in a specified direction in which $Q (\phi)$ is non-decreasing satisfies the same bound. Applying our bound to electrically charged black holes, we rule out a potential loophole in a recent proof [arXiv:2401.14449] of the Weak Gravity Conjecture in perturbative bosonic string theory.

We study the appearance of universality classes in overall weak-coupling infinite-distance limits in the conformal manifold of 4d ${\cal N}=4,2,1$ superconformal gauge theories at large $N$ and their relation to the type of weakly-coupled emergent string in the AdS bulk dual using brane models. We focus on the complete set of theories with simple gauge group, and provide explicit Hanany-Witten constructions for each of them, including those that have non-Einstein bulk duals. This establishes that the three universality classes found in arXiv:2410.07309 are determined by the number of NS5-branes becoming coincident in a suitable double-scaling limit required to obtain the SCFT. Furthermore, all theories within a given universality class descend from the same parent theory by performing orbifold/orientifold projections (with possibly a small number of extra flavors), which are subleading effects at large $N$. This explains the origin of the universality classes from a CFT perspective. Moreover, we argue that theories in the same universality class share the same closed-string background – generated by the double-scaled NS5-brane system – in which the backreaction of D-branes is expected to generate the AdS throat holographically dual to the SCFT. We describe the corresponding worldsheet theories, and find that the three kinds of emergent tensionless strings correspond to the 10d type IIB string, a subcritical string previously studied in a related context, and a novel kind of string which we characterize in detail. Our tools are not limited to this set of SCFTs, but can be naturally applied to more general theories, and allow us to study interpolating models yielding a network of SCFTs related by partial weak-coupling limits. We explicitly discuss the generalization of our results to large classes of theories with more than one gauge factor and even to some quasi-conformal gauge theories.

We perform a systematic survey of the Hagedorn behaviour at infinite-distance points in the conformal manifold of four-dimensional large-$N$ $\mathcal{N}=2$ Superconformal Field Theories admitting a Lagrangian description. Many properties of these theories can be understood in terms of the Lie algebra encoding the shape of their quiver. We find that in the overall-free limit, the Hagedorn temperature is determined by the largest eigenvalue of an affine or finite Cartan adjacency matrix. This defines two types of universality classes of theories sharing the same high-energy exponential growth of states characteristic of string-like spectra. The first and largest is the affine case, corresponding to orbifold and orientifold projections of $\mathcal{N}=4$ super-Yang-Mills, and all share the same temperature. The others fall into universality classes following an ADE classification with a temperature set by the dual Coxeter number, and can be obtained by deforming the affine case. Our results apply to all large-$N$ $\mathcal{N}=2$ quivers with any classical gauge symmetry, including those with matter charged beyond bifundamental representations. We further discuss the string-theoretic construction of these theories and some of the holographic implications, as well as how our methods extend to broad families of theories with less supersymmetry. We also consider limits where only part of the theory becomes free, and find lower and upper bounds on the exponential rate predicted by the CFT Distance Conjecture. Both these bounds and the Hagedorn temperature are set by the same eigenvalue, and when the quiver has a single gauge node the lower bound is saturated, giving a natural explanation for the three universality classes recently found in the literature.

Massive fields exchanged during inflation source cosmological collider features in the correlators of primordial curvature fluctuations. While their structure is fixed by the symmetries of inflation, the amplitude of such signatures is a priori unknown, though bounded by physical principles such as unitarity. We assess the observational viability of the scalar cosmological collider by combining precise numerical predictions derived using CosmoFlow with observational data from Planck bispectrum reconstructions. Working in the limit of weak quadratic mixing between the Goldstone and scalar sectors (as assumed by all previous searches), we find that perturbativity restricts the collider signals to be unobservably small, except for double- and triple-exchange configurations at low masses. Larger bispectra can be generated by increasing the mixing to non-perturbative (but still unitary) values: however, this distorts the signal, damping its amplitude and shifting the collider oscillations. Furthermore, strong mixing breaks the factorization of the bispectrum into a free amplitude and a fixed shape, and complicates both theoretical predictions and observational searches. Despite the challenges, we argue that strong mixing analyses are necessary to obtain meaningful constraints on the scalar cosmological collider from current and upcoming datasets.

We construct an explicit anomaly-free completion of a gauged baryon-number symmetry. The new gauge factor is \(U(1)_{\tilde B}\): when restricted to the Standard Model fields its charge \({\tilde B}\) coincides with ordinary baryon number, whereas in the full theory it becomes an extended baryonic symmetry acting on both the Standard Model and a secluded sector. We show that anomaly cancellation alone leaves a broad class of solutions, but that requiring consistent symmetry breaking, viable decays of the exotic states, the absence of stable coloured relics, a neutral dark matter candidate protected by a \(Z_2^{\rm DM}\) parity, and improved high-scale gauge-coupling unification strongly constrains the structure of the model. These requirements necessitate enlarging the minimal secluded fermion sector by additional scalar fields and Yukawa interactions, giving rise to a light pseudoscalar that plays an important role in the dark matter phenomenology. We implement the resulting renormalisable model in SARAH and analyse its spectrum and phenomenology with SPheno, MicrOMEGAs, SModelS, and HiggsTools. We identify viable regions of parameter space containing a heavy baryonic Z', an even heavier secluded sector, a neutral dark matter candidate compatible with relic-density and direct-detection constraints, and improved gauge-coupling evolution relative to the Standard Model. In these regions, the relic abundance is determined either by co-annihilation with nearby secluded states or by annihilation into light pseudoscalars from the extended scalar sector.

Spacetime torsion provides a natural extension of general relativity and may lead to black hole solutions that differ significantly from their Einsteinian counterparts. We investigate a class of Reissner-Nordström-like black holes in Poincaré gauge gravity, where the effective charge is generated entirely by spacetime torsion instead of an electromagnetic field. Within the physically relevant torsion sector, the spacetime exhibits a single-horizon structure, free from the inner horizons and extremal states characteristic of charged black holes. Using the sixth-order Wentzel-Kramers-Brillouin (WKB) approximation, Leaver's continued-fraction method, and the eikonal correspondence between quasinormal modes and unstable null geodesics, we study scalar perturbations and spin-2 test fields on the torsion-modified background. We find that increasing torsion decreases both the oscillation frequencies and damping rates, leading to longer-lived ringdown signals. We further compare the model predictions with Event Horizon Telescope observations of Sgr A* and M87*, along with representative LIGO-Virgo-KAGRA (LVK) ringdown scales, to derive constraints on the torsion parameter via a profile-$\chi^{2}$ analysis supplemented by Monte Carlo sampling. Although the resulting bounds remain consistent with the Schwarzschild limit within current observational uncertainties, our results show that spacetime torsion leaves correlated imprints on both black hole shadows and ringdown observables.

We analyse the initial-value problem of metric higher-derivative effective theories of gravity. We show that any such theory whose characteristic velocities are independent of derivatives of the metric is intrinsically weakly hyperbolic, independently of the gauge fixing. To show this, we identify the spin-$2$ physical sector directly from the characteristic equation; this can be done without introducing an order-reduced formulation, which greatly simplifies the computation. In this sector, every metric theory with more than two derivatives in the equations of motion contains a weakly hyperbolic block. Since this obstruction is physical, no choice of gauge or constraint addition can remove it, providing a structural explanation for the failure of strong hyperbolicity in this broad class of theories.

In this paper, we study codimension-two holography in a de Sitter (dS) wedge setup, based on the idea of wedge holography. We consider a $d+1$-dimensional Anti-de Sitter (AdS) bulk spacetime bounded by two end-of-the-world branes with $d$-dimensional de Sitter geometry. We propose that this configuration is holographically dual to a conformal field theory (CFT) living on a $d-1$-dimensional sphere. Our computations of the partition function and holographic entanglement entropy support this duality and indicate that the dual CFT is non-unitary. We also analyze the mass spectrum in dS wedge holography. We verify the first law of entanglement entropy within this framework. Finally, we make use of the island prescription to study the Page curve in a simplified model within our dS wedge holography framework.

We investigate linear and nonlinear primordial perturbations in an anisotropic Dirac-Born-Infeld (DBI) inflationary model with a non-vacuum initial state. Using the Arnowitt-Deser- Misner (ADM) formalism, we expand the action up to second and third order in the curvature perturbation and derive the corresponding scalar and tensor power spectra, as well as the bispectrum and the equilateral non-linearity parameter \(f_{NL}^{\mathrm{equil}}\). The effects of anisotropic corrections and non-Bunch-Davies (non-BD) initial conditions are incorporated through the slow-roll sector and Bogoliubov coefficients. For the numerical analysis, we consider an intermediate expansion scenario together with a phenomenological ansatz for the excited-state occupation number \(N_k\). By comparing the model predictions with recent observational datasets, including Planck2018 TT, TE, EE + lowE + lensing + BK18 + BAO and DESI+CMB+DESY5 data, we identify observationally viable regions in the parameter space of the model. Our analysis indicates that the anisotropic DBI scenario with non-vacuum initial conditions can remain compatible with current constraints on the scalar spectral index, tensor-to-scalar ratio, and equilateral non-Gaussianity for suitable ranges of the anisotropy parameter \(c\) and the initial-state parameter \(N_{k,0}\).

We study the low-temperature expansion of the disk partition function $Z(\beta)$ of the double-scaled SYK model (DSSYK) at fixed coupling $\lambda=2p^{2}/N$, where $N$ is the number of Majorana fermions and $p$ is the number of fermions in each interaction term, both taken to infinity. We show that the exact Bessel-function representation of $Z(\beta)$, expanded at large argument (corresponding to low temperature), can be organized in terms of the classical ring of quasi-modular Eisenstein series $E_{2},E_{4},E_{6}$ and their differential identities. Exploiting the modular $S$-duality properties of this ring, we derive the semiclassical (small $\lambda$) low-temperature expansion of $Z(\beta)$, splitting it into a perturbative tower and a non-perturbative sector controlled by $\widetilde q=e^{-4\pi^{2}/\lambda}$. At each order in $\widetilde q$, we determine the non-perturbative correction in closed form up to second order in $\lambda$; the resulting series resums into a compact expression in the same Eisenstein series, extending previous semiclassical results beyond their strict $\beta\to\infty$ limit. We further show that this entire structure follows from a single, exact differential equation coupling a modular derivative to derivatives with respect to temperature. Finally, we prove that the non-perturbative sector of $Z(\beta)$ is exactly supported, to all orders in $\lambda$, on the same exponents as the on-shell actions of known bilocal-Liouville saddles of the DSSYK Schwarzian limit, pointing to a well-defined bulk origin for these non-perturbative corrections.

Analytic infinite derivative gravity theories provide a renormalizable and ghost-free description of gravity around covariantly constant backgrounds. These theories can have non-singular bouncing Universe solutions. In this paper we aim to address a question whether it is possible to realize a bouncing solution without the presence of a ghost or a tachyon instability in this framework. We perform a detailed analysis of degrees of freedom in $(1+3)$ formalism around Minkowski and de Sitter space-times. As a result it becomes clear that on a very general basis one cannot construct an instability free bounce without a negative cosmological constant. An analysis of known bouncing solutions in this model shows that an analyticity of higher derivative form factors in combination with solutions parameters result in the presence of a ghost radiation. Being motivated by the idea of resolving the cosmological singularity problem we proceed by analyzing scalar and tensor modes anyway. Scalar modes appear to not influence Cosmic Microwave Background observations at all, while tensor modes spectrum is computed and the corresponding implications are discussed.

We solve the semiclassical Einstein equations for an evaporating Schwarzschild black hole in closed form, obtaining its backreacted geometry in 3+1 dimensions. This is achieved by a reformulation of the Hadamard renormalization prescription, which admits explicit stress-energy tensors for scalar quantum fields in 3+1-dimensional curved spacetimes without the standard mode-sum construction. The Unruh-like states we construct reproduce the Hawking flux at future null infinity and the associated ingoing negative-energy flux at the horizon, yielding the first analytical quasi-stationary solution describing black-hole evaporation in four-dimensional semiclassical gravity. The resulting geometry exhibits a timelike apparent horizon, providing a new analytical setting to study the causal structure of black-hole evaporation and its connection with the information-loss issue. Our results open a new route to semiclassical backreaction in four dimensions, extending the level of analytical control previously available only in two-dimensional effective models.

We set up a bootstrap workflow to study four-point conformal integrals in position space, using leading singularities, single-valued multiple polylogarithmic ansätze and boundary data from expansion by regions. These four-point conformal integrals are general in the sense that they are generated by the four-point projections of all possible $f$-graphs, including all non-planar $f$-graph sectors. For three-loop cases, fourteen of the fifteen inequivalent integrand basis can be directly calculated by HyperlogProcedures and the last one is fixed by Gram identity. Then we concentrate on how far the bootstrap workflow can go for four-loop cases, though it works for three-loop cases as well. We show that integrals with several leading singularities can be made tractable by decomposing them into pieces with simpler cut structure. Some four-loop integrals which can not be calculated or very hard to be calculated by other methods for now are obtained in this way. We also provide a package with skill files which is suitable to be read and used by current AI models.

We study timelike entanglement entropy and timelike subregion complexity in localized black holes with asymptotic AdS3*S3*T4 geometry, focusing on the black-pole solution. Unlike the BTZ solution, the black pole exhibits a nontrivial dependence on the internal sphere through the functions $K_y(r,\theta)$ and $G(r,\theta)$. Both observables are constructed from spacelike and timelike Lorentzian branches, but they probe the geometry in different ways: timelike entanglement yields a complex lifted area, while timelike complexity gives a real, finite renormalized volume. We employ a localized timelike prescription in which the branch profile is built at an angular label $\theta_0$ and subsequently lifted over the physical internal angle $\theta$. In the large-$r$ regime, the leading angular dependence drops out, recovering the expected short-interval behaviour. In the exact black-pole geometry, the temporal families become non-monotonic, making a fixed-boundary-interval selection essential. As the boundary interval increases, the selected branches move inward and become sensitive to the localized cap-horizon transition region. These results demonstrate that timelike Lorentzian observables probe localized-geometry effects that are absent in BTZ and in the leading large-$r$ description.

We study chiral symmetry and singlet $U(1)_A$ symmetry in QCD in a background magnetic field using lattice QCD. We first clarify the neutral-sector symmetry structure in a pure magnetic background, where the unequal electric charges of the light quarks explicitly reduce the non-singlet flavor symmetry. We identify the neutral-pion–sigma susceptibility difference, $\chi_{\pi^0}-\chi_\sigma$, as the chiral-partner splitting associated with the surviving neutral non-singlet axial symmetry, and the neutral-pion–delta susceptibility difference, $\chi_{\pi^0}-\chi_{\delta^0}$, as the singlet $U(1)_A$ partner splitting. We also discuss the disconnected contribution to the neutral-pion susceptibility and its continuum constraint. Numerical results are obtained on fixed-scale $(2+1)$-flavor HISQ ensembles with $m_l=m_s^{\rm phys}/10$, corresponding to a pion mass of about $220~{\rm MeV}$ at vanishing magnetic field. We find that the neutral chiral-partner splitting increases with the magnetic field strength $eB$ at low temperature and decreases at sufficiently large $eB$ near the crossover, providing susceptibility-splitting counterparts of magnetic catalysis and inverse magnetic catalysis, respectively. The singlet $U(1)_A$ partner splitting shows an analogous low-temperature enhancement and large-field suppression near the crossover, with the suppression setting in at larger $eB$ and remaining milder than in the chiral channel. These results provide a first lattice-QCD study of neutral-sector probes of chiral and singlet $U(1)_A$ partner susceptibility splittings in background magnetic fields.

We develop a non-nested Bethe ansatz description of rational $\mathfrak{gl}_\ell$ spin chains in the vector representation. Starting from the quantum spectral curve and the separation-of-variables framework, we derive closed systems of Bethe equations involving only the momentum-carrying Bethe roots. The construction is worked out explicitly for the $\mathfrak{gl}_3$ and $\mathfrak{gl}_4$ spin chains and then generalized to arbitrary rank. A central result of this work is the identification of a recursive hierarchy associated with the fundamental transfer matrices. The hierarchy is generated by regularity conditions of the lower transfer matrices and closes through a universal rank-$\ell$ equation $\mathcal{R}_{\ell}=0$. This equation replaces the final level of the conventional nested Bethe ansatz and eliminates all auxiliary Bethe roots. Consequently, the complete spectral data of an eigenstate are encoded solely in the first Baxter polynomial $Q_{1}(u)$. We further obtain explicit expressions for the eigenvalues of all fundamental transfer matrices in terms of the momentum-carrying roots alone. The resulting formulation provides a compact characterization of the spectrum of rational $\mathfrak{gl}_\ell$ spin chains and reveals a direct connection between the quantum spectral curve, transfer-matrix fusion relations, and a truncated $Q$-system underlying the non-nested description. Finally, we investigate the quasi-classical (Gaudin) limit of the non-nested Bethe equations. For the $\mathfrak{gl}_3$ spin chain, we show that the leading non-trivial contribution gives rise to Gaudin equations whose pole-free form naturally defines a scalar third-order $\mathfrak{gl}_3$ oper.

We present an exact solution describing multi-rotating black holes in 4D Einstein-Maxwell-dilaton theory, which can be obtained from 5D Kaluza–Klein theory via dimensional reduction. The solution represents a multi-centered configuration of rotating black holes carrying both electric and magnetic charges, with each black hole possessing a non-aligned angular momentum. This work generalizes our previous solution for black holes with aligned angular momenta to the more general case of non-aligned angular momenta. It includes, as special cases, the Majumdar–Papapetrou solution, the recent multi-centered rotating black hole solutions of Teo and Wan, and our previous solution with unequal electric and magnetic charges. The resulting spacetimes are free of curvature singularities and closed timelike curves, both on and outside the horizons, provided that the magnitude of the spin angular momentum of each black hole remains below a certain upper bound.

We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.

In this paper, we considered two-particle variants of the N-extended Euler-Calogero-Moser and Calogero models. Due the translation invariance, the center of mass can be decoupled (together with the corresponding fermions), leaving us with specific superconformal mechanics. Additional bosonic variables (spin variables) can easily be incorporated into the supercharges and the Hamiltonian. In the case of the Euler-Calogero-Moser model, the supersymmetry in the two-particle cases admits an unexpected extension from Osp(N|2) to SU(1,1|N) superconformal symmetry. The case of the Calogero model leads to purely Osp(N|2) superconformal mechanics. The way to get rid of the well-known problems along this path is to have a higher number of fermions present in the system.

We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.

In this manuscript, we propose a novel topological framework based on the heat capacity of black holes to investigate the topology of thermodynamic multicritical points. We construct a two-dimensional thermodynamic vector field whose isolated zeros correspond to the critical points of the system. The local topology of each critical point is characterized by its Brouwer degree, which serves as a locally conserved topological quantity. Applying this formalism to several AdS black hole solutions, we demonstrate that each system possesses a globally conserved topological charge. Although the number of thermodynamic critical points changes as the thermodynamic parameters are varied, the total topological charge remains invariant throughout the evolution. We show that these topological transitions are governed by the creation or annihilation of topologically neutral defect pairs carrying opposite Brouwer degrees. Our results provide a unified topological framework for understanding the emergence, evolution, and classification of thermodynamic multicritical points in black hole systems.

We use the large $N$ critical point formalism to examine the interplay of supersymmetry and chiral symmetry on the location or otherwise of multiple zetas in the renormalization group functions of several related field theories. In particular we determine that the anomalous dimension of the matter field of the Lagrangian corresponding to the bosonic sector of the $O(N)$ Wess-Zumino is free of multiple zetas to $O(1/N^3)$.

We derive the Belinfante–Rosenfeld symmetrization procedure from the metric-affine conservation law by means of an affine lift of flat-spacetime field theories. Following minimal coupling to an independent affine connection, variation of the action with respect to the connection defines the hypermomentum current. Taking the flat-spacetime limit of the resulting conservation law, we recover the Belinfante–Rosenfeld relation, with the divergence of the hypermomentum current reproducing the Belinfante improvement term. We thoroughly study the form of the couplings with this property and their physical significance. The construction is illustrated for Quantum Electrodynamics and Quantum Chromodynamics.