Papers

We investigate the small circle, or high temperature, limit of the supersymmetric index identities for the three-dimensional abelian mirror symmetry of SQED. There exist two possible limits, depending on how the parameters of the theory are scaled with the radius of the circle. In both cases the result is qualitatively similar. One side always reduces to the sphere partition function of a two-dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model (GLSM). The opposite side has a two-fold interpretation, either as the sphere partition function of the Landau–Ginzburg (LG) model that is Hori–Vafa dual to the GLSM, or as a Coulomb gas integral for a correlation function of Liouville or Toda CFT. This approach thus provides a systematic way to generate integral identities between partition functions of GLSMs on the one hand, and partition functions of LG models or CFT Coulomb gas integrals on the other. The latter perspective finds useful applications in the recently proposed 2d/2d correspondence, which relates sphere partition functions of unitary 2d $\mathcal{N}=(2,2)$ theories and correlation functions of non-unitary 2d CFTs that both descend from compactifications of a unitary 4d $\mathcal{N}=2$ SCFT. We present an example based on the $(A_{k-1},A_{N-1})$ Argyres–Douglas theories, where the CFT is a non-unitary minimal model. We also give a purely two-dimensional derivation of the identities obtained in the small circle limit which is inspired by the Kapustin–Strassler piecewise derivation of 3d abelian mirror symmetry.

We argue that the gravitational path integral for rotating black holes is periodic in the angular velocity, implying the quantization of angular momentum in arbitrary dimensions for either asymptotically flat or AdS boundary conditions. In AdS$_3$, this periodicity is a consequence of the boundary mapping class group. In higher dimensions, the periodicity arises from an infinite family of saddles labeled by integer shifts of the angular velocity unrelated to the boundary mapping class group; summing over these saddles enforces quantization independently of any large boundary diffeomorphism. We construct these saddles explicitly for Kerr-Newman black holes in both asymptotically flat space and AdS$_4$, and observe that even the path integral for the 4D Schwarzschild black hole, typically the simplest case, receives contributions from an infinite set of rotating saddles.

Construction of physically realistic theories admitting regular black hole solutions remains an important open problem in gravitational physics. While theories with electromagnetic fields minimally coupled to gravity have been extensively studied over the past two decades, theories with nonminimal couplings remain comparatively unexplored. We investigate theories containing the interaction terms $R F_{ab}F^{ab}$, $R_{ab} F^a_{\ \, c} \, F^{bc}$ and $R_{abcd} F^{ab} F^{cd}$, which generically arise in low-energy effective Lagrangians. We prove that magnetically charged regular black holes are excluded, except possibly for finely tuned choices of coupling constants, and argue that a similar conclusion applies to electrically charged regular black holes. We further show that similar conclusions hold for Lagrangian terms of the form $f(R,F_{ab}{\star F}^{ab})$.

We derive spectral identities involving the Laplace spectrum and the integrals of products of eigenfunctions on flat tori and orbifolds. Using semidefinite programming, we derive upper bounds on sums of squares of triple products from these spectral identities, following the approach of the conformal bootstrap. Physically, these upper bounds give constraints on sums of squares of cubic coupling constants in toroidal compactifications of higher-dimensional field theories. For Euclidean lattices, one of the bootstrap bounds leads to an upper bound on the mean square number of minimal vectors that are minimal distance from each minimal vector, divided by the kissing number of the lattice. By finding exact functionals for the semidefinite programming problems, we prove that this bound is saturated in 2, 4, 8, and 24 dimensions by the hexagonal lattice, the $D_4$ lattice, the $E_8$ lattice, and the Leech lattice, respectively.

We develop an ambitwistor-space formulation of conserved spinning correlators in four-dimensional CFTs. We show that conformal symmetry and conservation are trivialised by the ambitwistor Penrose transform, and construct the two- and three-point ambitwistor correlators explicitly. We further propose a simple formula for projecting onto parity-even and parity-odd sectors, and verify it in several non-trivial examples. The resulting correlators furnish a natural basis compatible with a boundary double copy for arbitrary spin. At three points, we show that they localise on degree-three curves in a two-twistor representation. We also explain how the formalism incorporates boundary propagators for unitary operators of integer conformal dimension, and extend it to conformally coupled scalars.

We study dynamical mass generation of a fermion with and without a bare mass by coupling with a massive vector field in two-dimensional space-time. To estimate a non-perturbative effect on the fermion mass, we employ the Schwinger-Dyson equations in the lowest-ladder approximation, which are solved by an approximated analytical method and also by a numerical method. We define a purely dynamical mass as a remnant after subtracting the bare mass from a total dynamical mass. We clarify dependence of the purely dynamical mass on the bare mass of the fermion in various region of a coupling constant. Especially we find that the purely dynamical masses growing from the different bare masses coincide with each other at a specific value of the coupling constant where a kind of a duality relation on the bare masses is satisfied.

We study memory effects in quantum cosmology by extending the semiclassical Wheeler-DeWitt framework beyond its usual local form. The main idea is to introduce a causal memory kernel at sub leading order, rather than imposing fractional derivatives directly by hand. In this setting, fractional time evolution appears as an effective description of the underlying nonlocal dynamics. We apply the framework to cosmological perturbations in de Sitter space and find a correction to the primordial power spectrum with a characteristic $k^{3/4}$ scaling. This contribution mainly affects high $l$ CMB temperature anisotropies, in contrast with standard semiclassical quantum gravitational corrections, which are strongest at large angular scales. We also discuss how the same memory-dependent dynamics may affect primordial non-Gaussianity, producing scale dependent corrections to the bispectrum and possible deviations from the usual squeezed limit consistency relation. Since the memory coefficient controls short scale power, it may also influence structure formation and could require some tuning in order to give phenomenologically acceptable astrophysical environments. Finally, we suggest that a cyclic extension of the Hawking-Hartle no-boundary proposal may provide a setting in which the effective memory strength can evolve across successive cosmological histories. In this way, the framework gives a concrete realization of fractional quantum cosmology based on memory effects and also points to possible observational signatures of nonlocal quantum gravitational dynamics.

The one-loop five-point function of stress tensor multiplets in N=4 super Yang-Mills theory in four dimensions has previously been studied by integrability methods. The finite-size viz gluing corrections defining it were originally matched on the known field theory result - establishing many features of the formalism on the way - and later to a good extent also analytically evaluated. For the first time, we present a full analytic evaluation of all processes. The starting point is the re-summation of series of residues into Euler integrals. These are directly integrated where possible or otherwise recovered from intersection theory for generalised hypergeometric functions.

We construct a graphical coaction for Friedmann-Robertson-Walker (FRW) integrals at all loop orders in conformally-coupled scalar theories with non-conformal polynomial interactions. Our construction makes use of intersection theory in the context of (partial/relative) twisted (co)homology, which we use to decompose FRW integrals (and their discontinuities and derivatives) into building blocks that can be represented as decorations of the original Feynman diagram. This facilitates a purely graphical description of the coaction, up to rational prefactors that can be read off from the graph. Our construction provides a comprehensive combinatorial framework for dissecting the analytic properties of cosmological observables; in particular, we demonstrate that the combinatorics of the differential equations that govern FRW integrals – their so-called kinematic flow – is a natural consequence of our coaction. We have also developed a user-friendly web application that computes the graphical coaction of any graph: https://frwcoaction.ca. Whenever possible, the web application also computes the differentials and discontinuities. A Mathematica notebook with the same functionality is also hosted at on a public GitHub repository.

We study the cosmological dynamics of the thermal scalar the winding string mode that becomes massless at the Hagedorn transition by coupling it to the string-frame gravi dilaton effective action. This provides a field-theoretic framework for investigating winding mode dynamics near the Hagedorn temperature and their role in string cosmology. Below the Hagedorn temperature, the phase space contains static configurations in which the thermal scalar balances the shifted dilaton evolution. These configurations are boundary states rather than attractors, and when the thermal scalar mass depends on the scale factor, winding mode back reaction opposes expansion and can reverse it. Above the Hagedorn temperature, the tachyonic thermal scalar generates negative effective energy density while preserving the null energy condition, enabling branch changes of the Brustein Veneziano type. These transitions do not provide the graceful exit required to connect the Hagedorn phase to standard cosmological evolution. At the Hagedorn temperature itself, the quadratic effective theory breaks down and higher order interactions become essential. Because the thermal scalar originates as a Euclidean order parameter, our Lorentzian treatment should be viewed as an effective dynamical model of the Hagedorn transition. Within this framework, the thermal scalar clarifies the dynamical structure surrounding the Hagedorn transition and shows how the Hagedorn exit problem cannot be resolved within the quadratic effective theory alone.

We develop an on-shell framework for thermal dissipation and radiation by macroscopic objects, whose large degeneracy of internal states is encoded in their entropy. In this framework, equilibrium asymptotic states are represented as on-shell particles, while non-equilibrium processes are described by on-shell transition amplitudes between them. A central observation is that spinning states remain essential even for macroscopically non-rotating objects. Consistency with macroscopic symmetries then implies spin universality, whereby all spinning states are governed by a single universal coupling. A key consequence is that absorption and emission probabilities are controlled by the same coupling, yielding local detailed balance directly from on-shell data. Applied to black holes, our framework reproduces the thermal emission spectrum and relates the Hawking temperature to the condition of maximal absorption consistent with unitary time evolution.

We formulate a local geometric criterion for weak cosmic censorship in black hole overcharging and overspinning thought experiments. Under the null convergence and generic conditions, matter injection turns a horizon cross section into a closed trapped surface. Any final spacetime unable to accommodate this surface is ruled out. This trapped surface criterion excludes superextremal Reissner-Nordström, Reissner-Nordström-de Sitter, and Kerr-Newman final states, as well as Weyl-class naked singularities. Our criterion does not rely on asymptotic charges or on an extremal condition characterizing naked singularities.

ZX calculus provides a graphical formalism for reasoning about quantum processes, built from two interacting Frobenius algebras associated with the Z and X bases of a qubit. While it has found widespread application in quantum information and computing, its relationship to quantum field theory has only recently begun to be explored. In this work, we further develop this connection by providing a generalization of ZX calculus to two-dimensional Yang Mills theory with a compact gauge group. The key observation is that both frameworks can be organized around the Hopf Frobenius algebraic structure associated with a group algebra, which can in turn be described by the diagrammatics of two dimensional topological quantum field theory. Given the well known relationship between gauge theory and gravity in two and three dimensions, our work paves the way for applications of ZX to low dimensional gravity.

We study the one-loop correction to the entropy of near-extremal black holes in three-dimensional massive gravity at the special point where the theory exhibits a unique maximally symmetric vacuum and non-constant curvature hairy black holes can achieve extremality even in the static case. Focusing on the near-horizon AdS$_2\times S^1$ geometry, we evaluate the contribution of boundary graviton modes that become exact zero modes in the extremal limit. We show that the resulting one-loop partition function generates logarithmic corrections to the semiclassical entropy, providing a new extension to higher-curvature gravity of what has been recently obtained for near-extremal black holes in General Relativity.

When matter fields are integrated out in a large N approximation, the conformal anomaly induces an effective action up to conformally invariant correction terms. In the present work, we consider the implications on black hole evaporation of such a term involving a conformal invariant found by Fefferman and Graham. Working in an approximation where the spacetime is static, we compute the induced stress tensor around a Schwarzschild black hole. The boundary conditions select an Unruh-like asymptotic sector, but not a unique stress tensor. A new one-parameter family of quantum hair emerges which changes the stress tensor in the near-horizon region. This suggests a new semiclassical mechanism by which information about black hole formation could be encoded outside the horizon.

This paper develops an epistemological constraint on quantum gravity grounded in the empirical meaning of general relativity. The central claim is that a complete recovery of general relativity requires an effective metric, a continuum limit, or Einstein-like dynamics together with the physical conditions under which relational geometrical quantities can be objectively determined. These conditions concern the dynamical stability of measuring devices and reference systems, causal accessibility among physical systems, record formation, and invariance under admissible descriptions. In classical general relativity, they are usually implicit in the use of clocks, rods, light signals, freely falling bodies, detectors, and gauge-invariant observables. In quantum gravity, however, they become non-trivial because spacetime geometry may be emergent, effective, thermodynamic, relational, or frame-dependent. This claim is developed through four cases: Rindler horizons and the Unruh effect, black-hole thermodynamics and Jacobson's equation-of-state derivation, gravitational-wave detection, and Weyl and conformal gravity. The latter is discussed as a critical limiting case in which conformal invariance raises a sharp question about whether scale-dependent measurements of space and time can be physically fixed. Implications for quantum gravity are also discussed using emergent gravity and quantum reference frames as examples. The perspective developed in the study suggests a general epistemological constraint on quantum gravity: any viable approach must recover the physical possibility of objective geometrical measurement together with geometry itself.

Yang-Mills theories at $\theta$ and $\theta+2\pi$ are unitarily equivalent, but their $2\pi$ periodicity has a nontrivial realization. Recent developments in generalized symmetries rigorously prove that confinement vacua at $\theta=0$ and $2\pi$ should belong to different symmetry-protected topological (SPT) states with the $1$-form center symmetry. For its examination, we measure the Wilson-'t Hooft loop operators at $\theta=2\pi$ for the $SU(2)$ Wilson lattice gauge action and discuss their long-distance behaviors. This requires us to identify the gauge topological charge in the presence of defects, and we employ the $1$-form covariant DBW2 gradient flow to smear lattice gauge fields. We find a clear perimeter-law signal for the dyonic Wilson-'t Hooft loop at $\theta=2\pi$, providing numerical evidence in the pure $SU(2)$ Yang-Mills theory for the theoretically expected dyon condensation at $\theta=2\pi$.

In QCD sum rules for light-quark systems, infrared (IR) divergences can appear in the Wilson coefficients of certain condensates. These divergences manifest explicitly in the coordinate-space expressions of the light-quark propagators. We propose an improved method to eliminate these IR divergences at the propagator level and present a subtraction formula that implements this procedure. Compared to the existing methods that rely on the mixing between quark and gluon condensates of the same dimension to eliminate IR divergences, this method is more intuitive and easier to apply in practical QCD sum rule calculations.

We study Yang-Mills theory coupled to a particle on a cylinder, where gauge invariance and compactness reduce the dynamics to a finite dimensional quantum system. In the Abelian case, this yields a model equivalent to the Landau problem on a torus, with a degenerate ground state structure. We generalize this construction to non-Abelian gauge groups and show that, for SU(N), the system reduces to a one dimensional quantum many body problem with a singular Calogero-Sutherland-type interaction.

The black hole information paradox originates from the thermal character of Hawking radiation, which appears to erase information about the collapsing matter. However, thermality constrains only observables defined at a single time and leaves the structure of temporal quantum correlations largely unexplored. Here we show that multi-time quantum-field correlations provide a concrete mechanism for the survival of pre-collapse information in black hole evaporation. Using a two-dimensional model of gravitational collapse and evaporation, we demonstrate that late-time multi-time correlations are not fully reproduced by the Unruh vacuum. In particular, they contain a contribution that depends explicitly on parameters characterizing the pre-collapse state, despite the thermal character of the asymptotic radiation. Our results identify measurable multi-time correlations as carriers of information in Hawking radiation and suggest that formulations of the black hole information paradox based solely on single-time observables are incomplete.

In the present work, we study the absorption cross section of a Schwarzschild black hole for a massive vector field over arbitrary frequencies. Working in the Frolov-Krtouš-Kubizňák-Santos (FKKS) basis, we show how the conserved flux of the normalized Proca field naturally leads to the usual definitions of the absorption cross section in terms of the reflection and transmission coefficients. We then numerically compute these quantities over arbitrary frequencies. In contrast to the massless (photon) case, massive vector bosons exhibit new features arising from the field mass. In particular, the mass term introduces a longitudinal degree of freedom in addition to the transverse modes. Furthermore, it leads to a scalar-type branch in the even parity transverse modes, thereby breaking the usual degeneracy with the odd parity sector found in the massless case. We illustrate how these characteristics manifest themselves in the transmission and absorption spectrum. Given the recent developments in the study of ultralight bosonic fields in black hole spacetimes, the present analysis of the transmission properties of massive vector bosons bears particular significance.

We derive a class of vacuum regular black holes inspired by effective loop quantum gravity dynamics and extend the construction to asymptotically anti-de Sitter spacetimes. The derivation is based on a deparameterized Lemaitre–Tolman–Bondi formulation, where an auxiliary dust field is introduced only to define an internal time and does not act as a matter source. In spherical symmetry, the dynamics reduces to a set of independent radial shells, giving rise to a factorized shell Hamiltonian and to a Birkhoff-type property: for a fixed reconstruction function and cosmological constant, the static geometry is uniquely determined by the mass. Within this framework, we establish the conditions for curvature regularity at the center and construct several regular black hole models with de Sitter cores and corresponding models with anti-de Sitter cores. We then study their thermodynamics in the extended phase space, using the Hawking–Page transition to compare the de Sitter- and anti-de Sitter-core branches and show that their quantitative differences arise from the deformation of the physical outer-horizon branch rather than from regularity alone.

We analyze the flow of the background graviton propagator driven by the running of asymptotically safe form factors in four-dimensional quantum gravity at quadratic order in the curvature expansion. We construct the propagator in the $k=0$ limit and investigate its momentum dependence. The non-local form factors are then analytically continued to Minkowski spacetime, from which the corresponding Minkowskian propagator is obtained. We find a single pole at $q^2=0$ with positive residue and no additional ghost poles at this level of approximation. The corresponding Newtonian potential is found to be regular at $r=0$.

We prove the existence of Long-Range Order in a class of two-dimensional Euclidean lattice Gross-Neveu models with an even number of fermion flavors, covering three standard lattice discretizations, including naive and staggered fermions widely used in numerical studies. By performing a Hubbard-Stratonovich transformation, we map the fermionic systems to bosonic ones and establish Reflection Positivity for the resulting measures. Exploiting this structure, we combine Chessboard Estimates with a Peierls-type contour argument to prove Long-Range Order for the chirally charged fermion-mass bilinear $\overline{\psi}\psi$ at sufficiently small coupling and sufficiently large flavor number. Our analysis is robust with respect to the choice of lattice discretization and applies uniformly across different realizations of the same underlying continuum model. Moreover, we obtain uniform pointwise bounds on the bosonic two-point function, equivalently on the fermionic mass-mass correlator, showing that it is quantitatively controlled by the minimizers of the effective potential. This provides a fully rigorous and non-perturbative demonstration of Long-Range Order in lattice Gross-Neveu models and establishes a direct connection between the rigorous theory and its large-$N$ (mean-field) predictions.

Can a classically relevant stress-tensor deformation be exactly solvable, duality preserving, and physically causal? We construct an exact power-law family of nonlinear electrodynamics preserving electromagnetic duality, together with a parallel two-dimensional Lax-integrable realization. Its auxiliary geometry yields the full characteristic-cone phase diagram and a universal finite-energy fold. For the Maxwell seed, every nonzero relevant branch is acausal, whereas every causal branch is caustic-free; undeformed Maxwell theory is the only causal point in the relevant regime.

Extending the double copy of scattering amplitudes to more general physical quantities involving local gauge-invariant operators is a central open question. While progress has been made in the double copy of form factors (FFs) with a single-operator insertion, it has led to two intriguing features: poles that are spurious from the FF viewpoint become physical propagators in gravity, and FFs obey hidden factorization relations on these poles. This picture is difficult to generalize to FFs with multiple operator insertions due to even more complicated spurious pole structures. We resolve this problem by introducing a "dyeing" procedure that promotes color-singlet operators to adjoint colored states, while the original FF is recovered by the inverse "bleaching" (U(1) decoupling) operation. In this new picture, the spurious poles are propagators of the dyed state, and the hidden factorization relations follow from BCJ relations of the dyed amplitudes. For multiple operator insertions, this framework uncovers a new scalar-ordering structure that survives the double copy to gravity.

In the Cartan teleparallel formulation of gravity, a scalar field coupled to the torsion tensor can acquire an environment dependent effective mass. This gives rise to a screening effect: Inside dense bodies such as the Sun, the scalar field is suppressed, causing the mass varying neutrino mass to vary with local density. We investigate the impact of this torsion-induced screening on solar neutrino oscillations. The mechanism modifies the standard MSW resonance condition in a distinct way, leading to detectable shift in the flavor conversion probability. Using data from solar neutrino experiments (Super-Kamiokande, Borexino, SNO), we place constraints on the torsion-scalar coupling parameters. Our work provides concrete test of teleparallel gravity through mass varying neutrino oscillations.

In this work, we investigate how entanglement between two massive quantum particles trapped in harmonic oscillator potentials is generated after they interact with propagating modes of the quantized gravitational field. Specifically, we consider only the entanglement arising from the coherent contribution of the gravitational field to investigate its causal structure. We employ the Feynman-Vernon influence functional approach, within which the contribution of the coherent gravitational field to entanglement generation can be traced to the commutation relation of the gravitational field. Our analysis shows that entanglement does not arise instantaneously after the interaction begins. Instead, there is a time delay proportional to the separation between the two particles before entanglement begins to develop. This result shows that the entanglement arising from the coherent contribution of the gravitational field exhibits a causal structure. The magnitude of the resulting entanglement is generally very small. However, when the initial quantum states of the two particles are prepared as separable squeezed states, the resulting entanglement can be enhanced, with the magnitude of the enhancement depending exponentially on the squeezing parameter.

Quantum clocks can acquire relativistic phases from motional or gravitational proper-time differences, but reduced clock dephasing alone does not certify nonclassical proper-time histories. We formulate this distinction as a channel-certification problem. First, we show that any two-level single-time dephasing signal, including one generated by an effective quantum proper-time label, admits a classical random proper-time representation. We then define the convex set of classical mixtures of experimentally specified proper-time histories and prove a Choi-rank separation criterion for conditioned coherent history recombination. A two-branch Ramsey protocol gives explicit bright- and dark-port population witnesses outside this classical set. The certification is operational and relative to the specified history set: it rules out classical mixtures of the same implemented proper-time histories, not arbitrary classical protocols with different histories or controls.

We investigate the dynamical and optical properties of a higher-dimensional loop-quantum-corrected black hole in a de Sitter background. We first analyze the horizon structure and identify the admissible nonextremal black-hole domain bounded by the extremal and Nariai configurations, ensuring the existence of distinct inner, event, and cosmological horizons for the parameter sets considered. We then examine the scalar effective potential and show that the loop-quantum correction deforms the classical scattering barrier primarily in the strong-field region while preserving its characteristic single-barrier structure. The quasinormal modes of massless scalar perturbations are computed using time-domain evolution with Prony extraction, the matrix method, and the WKB approximation, showing good agreement among the three approaches. The time-domain waveform and its Prony and matrix-frequency reconstructions provide an additional direct consistency check of the extracted ringdown spectrum. We find that loop quantum corrections induce moderate shifts in the quasinormal spectrum, whereas the spacetime dimensionality has a much stronger impact, leading to higher oscillation frequencies and damping rates. The negative imaginary parts of all modes indicate dynamical stability against massless scalar perturbations within the explored parameter range. Comparison with the corresponding classical black-hole backgrounds shows that the quantum-corrected quasinormal spectrum remains continuously connected to the classical photon-sphere branch, with the loop correction producing quantitative rather than qualitative changes.