# Araya, Esper, Jia, Kulaxizi, Parnachev ## Bulkcone Singularities and Complex Geodesics \[Links: [arXiv](https://arxiv.org/abs/2602.12893), [PDF](https://arxiv.org/pdf/2602.12893)\] \[Abstract: [[0512 Thermal correlators|Thermal correlators]] in holographic CFTs on a sphere exhibit [[0163 Bulk cone singularity|bulk-cone singularities]] at points connected by null geodesics in the bulk. The [[0030 Operator product expansion|operator product expansion]] analysis of the stress-tensor sector of the correlator shows that there are analogous singularities at spacelike separation for thermal CFTs on a plane. We show that these are associated with complex null geodesics. There is a phase transition between the real and complex spacelike geodesics underpinning this picture. We also provide a phase-shift calculation of the position of these generalised bulk-cone singularities.\] # Banerjee, Dey, Dhar ## Boundary conformal field theory, holography and bulk locality \[Links: [arXiv](https://arxiv.org/abs/2602.04223), [PDF](https://arxiv.org/pdf/2602.04223)\] \[Abstract: We study bulk locality in a scalar effective field theory (EFT) in AdS background in presence of an end-of-the-world (EOW) brane. The [[0181 AdS-BCFT|holographic dual]] description is given in terms of a [[0548 Boundary CFT|boundary conformal field theory]] (BCFT). We compute the two point correlation function of scalar operators in the BCFT using the one-loop [[0109 Witten diagrams|Witten diagrams]] and compare its analytic structure with the constraints imposed by boundary [[0028 Conformal symmetry|conformal symmetry]]. We find that the loop-corrected correlator derived from a local bulk description is not fully compatible with BCFT expectations. This result places nontrivial constraint on bulk locality in holographic BCFT constructions and identifies BCFT correlators as sensitive probes of quantum bulk dynamics in presence of boundaries.\] # Boschetti, Campiglia ## An asymptotic proof of the classical log soft graviton theorem \[Links: [arXiv](https://arxiv.org/abs/2603.09844), [PDF](https://arxiv.org/pdf/2603.09844)\] \[Abstract: We present a derivation of the classical log [[0009 Soft theorems|soft graviton theorem]] within the asymptotic framework of Compère, Gralla, and Wei. The proof relies solely on Einstein equations near timelike, spatial, and null infinity, together with matching properties across these regions. The approach is fully covariant under time reversal and incorporates contributions from incoming soft radiation. In the absence of incoming memory one recovers the standard log soft factor, which features an asymmetry between future and past hard components. From an asymptotic perspective, the origin of this asymmetry lies in a long-known discontinuity of the gravitational field at spatial infinity.\] # Calkins, Pate ## Multi-particle Celestial Operator Product Expansions from the Boundary \[Links: [arXiv](https://arxiv.org/abs/2601.04329), [PDF](https://arxiv.org/pdf/2601.04329)\] \[Abstract: In [[0010 Celestial holography|celestial holography]], scattering particles in four-dimensional asymptotically flat spacetimes are dual to conformal primary field operators on the celestial sphere. Multi-particle celestial operators can be formed from regularized coincident limits of single-particle celestial operators. The singular terms in the [[0030 Operator product expansion|operator product expansion]] of multi-particle operators are shown to be determined entirely by the singular terms in the operator product expansion between single-particle celestial operators, as expected in a standard conformal field theory. Boundary operator product expansions in celestial holography are known to be dual to subtle [[0078 Collinear limit|collinear limits]] of bulk scattering amplitudes. The multi-particle operator product expansions derived from standard conformal-field theoretic techniques are shown to reproduce precisely the results from the corresponding bulk collinear limits in tree-level Yang-Mills and Einstein gravity. Finally, the coefficients of multi-particle celestial operator product expansions are derived from a third complementary method that enforces bulk four-dimensional translational invariance as a global symmetry of the celestial dual. The results of all three methods agree precisely.\] # Cheung, Sivaramakrishnan, Wilson-Gerow, Zhou ## On Perturbatively Dressed Observables \[Links: [arXiv](https://arxiv.org/abs/2605.26077), [PDF](https://arxiv.org/pdf/2605.26077)\] \[Abstract: A central lesson of gravity is that local observables are ill-defined. Coordinates themselves are a redundancy of description, so any particular point in spacetime is only meaningful once defined relationally by clocks, rulers, or asymptotic data. Despite extensive formal work on this subject, explicit calculations of the resulting gravitationally-[[0180 Dressing|dressed]] observables are more scarce. In this paper we perturbatively compute dressed matrix elements of local operators in electrodynamics and general relativity, including both potential and radiative photons and gravitons. Our expressions indicate that dressing is not ornamental: it universally induces kinematic singularities that can substantively reshape observables. We further show how dressing is mathematically equivalent to gauge fixing, as demonstrated by a dynamical temporal gauge in which the gauge-fixing vector is itself a geodesic fluid.\] # Czech, Shuai ## Renormalization Group is the principle behind the Holographic Entropy Cone \[Links: [arXiv](https://arxiv.org/abs/2601.02472), [PDF](https://arxiv.org/pdf/2601.02472)\] \[Abstract: We show that every [[0259 Holographic entropy cone|holographic entropy inequality]] can be recast in the form: 'some entanglement wedges reach deeper in the bulk than some other entanglement wedges.' When the inequality is saturated, the two sets of wedges reach equally deep. Because bulk depth geometrizes CFT scales, the inequalities enforce and protect the [[0209 Holographic renormalisation|holographic Renormalization Group]].\] # Drukker, Komatsu, Wallberg ## Crosscap Defects \[Links: [arXiv](https://arxiv.org/abs/2604.19868), [PDF](https://arxiv.org/pdf/2604.19868)\] \[Abstract: We introduce a novel class of [[0065 Defect CFT|defects]], termed crosscap defects, in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a $Z_2$ automorphism, and provide higher-codimension generalisations of CFT on real projective space ($RP^{d}$). Crosscap defects extend along a $p$-dimensional fixed locus of the $Z_2$ action and preserve an $SO(p+1,1)\times PO(d-p)$ subgroup of the conformal group. The two-point functions of operators in this setup exhibit three operator product expansion channels: bulk, image, and defect. These lead to several crosscap crossing equations, which we present. We analyse conformal block decompositions and show that the blocks are identical to defect CFT blocks up to a redefinition of cross ratios. As concrete examples, we study crosscap defects in the $O(N)$ model at the Gaussian and Wilson--Fisher fixed points in the $\varepsilon$-expansion. We compute explicitly the associated CFT data as a function of p and find that, unlike standard defects, displacement and tilt operators are absent for generic $p$. They provide examples of defect conformal manifolds without exactly marginal operators.\] # Engelhardt, Nagar ## A Quantum Singularity Theorem for the Evaporating Black Hole \[Links: [arXiv](https://arxiv.org/abs/2605.05326), [PDF](https://arxiv.org/pdf/2605.05326)\] \[Abstract: We prove a [[0225 Singularity theorems|singularity theorem]] in semiclassical gravity without assuming global hyperbolicity or the [[0480 Null energy condition|null energy]]/curvature condition; the former is replaced by the weaker causality conditions of stable causality and past reflectivity, and the latter is replaced as is standard by the [[0082 Generalised second law|Generalized Second Law]]. This establishes in particular that the standard models of evaporating black holes are singular - i.e. they are null geodesically incomplete.\] # Gamarnik, Pernice, Schmidhuber, Zlokapa ## The free energy limit of the SYK model at high temperature \[Links: [arXiv](https://arxiv.org/abs/2605.02768), [PDF](https://arxiv.org/pdf/2605.02768)\] \[Abstract: The [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties can be derived heuristically using a combination of the replica method and path integration techniques. Analyzing it mathematically rigorously, however, turned out to be notoriously difficult, even for basic questions such as computing the annealed free energy. In this paper we rigorously compute the free energy limit (annealed and quenched) for this model at high enough but constant temperature. Our results are in numerical agreement with the results derived by physics methods. Remarkably, though, our method of proof is novel and is different from the physics approach. It is based on (a) the theory of the component structure of sparse random graphs and (b) a variant of the cavity method, used widely in prior rigorous and heuristic treatments of classical spin glasses.\] # Giombi, Li, Shan ## Bouncing singularities and thermal correlators on line defects \[Links: [arXiv](https://arxiv.org/abs/2603.11012), [PDF](https://arxiv.org/pdf/2603.11012)\] \[Abstract: Thermal correlators in holographic conformal field theories are known to exhibit [[0672 Singularity signatures from boundary correlators|singularities]] in complex time, sometimes referred to as ''bouncing singularities", which are believed to be related to bulk geodesics probing the black hole interior. These singularities correspond to exponentially suppressed contributions in the high-frequency limit of the thermal correlators. We revisit in detail the calculation of retarded two-point functions of local operators dual to bulk scalar fields in the planar AdS black hole background. We confirm that these correlators develop bouncing singularities, and highlight the agreement of two independent methods: a large frequency WKB analysis with infalling boundary conditions at the horizon; and an asymptotic OPE analysis that relies only on the near-boundary expansion, without any direct input from the black hole interior. We then extend these calculations to the case of the retarded two-point function of displacement operators on a Wilson line in the finite temperature gauge theory. This is computed holographically by solving the wave equation for the transverse fluctuations of the dual string worldsheet in the planar AdS black hole background. We find that these defect correlators also exhibit bouncing singularities, and again observe exact agreement between the WKB analysis sensitive to the black hole interior and the asymptotic OPE analysis. This agreement suggests that the bouncing singularities and the corresponding OPE data encode a universal high-frequency structure of the retarded correlators, and we propose a factorization formula that encodes the deviations from this universality.\] # Giribet, Sivilotti ## The disk 1-point function in timelike Liouville theory \[Links: [arXiv](https://arxiv.org/abs/2603.12084), [PDF](https://arxiv.org/pdf/2603.12084)\] \[Abstract: We compute the disk 1-point function in [[0622 Timelike Liouville|timelike Liouville theory]]. Using the Coulomb gas formalism and analytically continuing in the number of screening operators, we derive an explicit formula, which is shown to satisfy the correct reflection symmetry, to have the expected self-dual properties, to fulfill the bootstrap shift-equations, and to reduce to previous known results in the appropriate limits. In the limit of zero cosmological constant, our result reproduces the one recently obtained in [arXiv:2505.09390](https://arxiv.org/abs/2505.09390).\] # Grozdanov, Valach, Vrbica ## Bouncing geodesics, black hole singularities, and singularities of thermal correlators \[Links: [arXiv](https://arxiv.org/abs/2603.15598), [PDF](https://arxiv.org/pdf/2603.15598)\] \[Abstract: Bouncing geodesics have been used as valuable probes of black hole [[0672 Singularity signatures from boundary correlators|singularities]]. In the dual boundary theory, the presence of bouncing geodesics is encoded in the analytic structure of correlation functions. Thus, when their existence is related to the presence of a black hole singularity, this presents a practical holographic framework to analyse, diagnose, and classify spacetimes with curvature singularities. To make this intuition precise, we use the Hadamard theory of hyperbolic differential equations to prove that both bulk and boundary retarded propagators diverge whenever two points can be connected by a null geodesic. We clarify why this statement remains valid beyond the geodesic regime (for operators of any dimension) and examine how holographic renormalisation modifies the structure of the dual propagator. We also present a general characterisation of bouncing geodesics and the associated singularities in correlation functions for arbitrary spacetimes. Furthermore, we compare the analytic structure of the correlators in position and momentum space and discuss explicit examples. Finally, we demonstrate the validity and concrete limitations of the bouncing geodesic approach to the study of black hole singularities. In particular, we show an explicit example of a black hole in the self-dual linear axion model, which has a curvature singularity despite the absence of bouncing geodesics.\] # Hatsuda, Shiga ## Exact WKB and Quantum Periods for Extremal Black Hole Quasinormal Modes \[Links: [arXiv](https://arxiv.org/abs/2605.01321), [PDF](https://arxiv.org/pdf/2605.01321)\] \[Abstract: We apply exact WKB analysis to the spectral problem arising in black hole perturbation theory. The boundary conditions for quasinormal modes lead to exact quantization conditions for the complex frequencies. To solve these conditions, one needs to evaluate the so-called quantum periods, or Voros symbols. For scalar perturbations of extremal Reissner--Nordström and Kerr black holes, we compute these quantities up to very high orders in the WKB expansion and perform Borel--Padé resummation. The resulting resummed quantization conditions successfully reproduce the correct [[0325 Quasi-normal modes|quasinormal mode]] frequencies with high precision.\] # Jafferis, Wang ## The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity \[Links: [arXiv](https://arxiv.org/abs/2604.09396), [PDF](https://arxiv.org/pdf/2604.09396)\] \[Abstract: We study a model of [[0002 3D gravity|3d gravity]] relevant to the open sector of a CFT [[0154 Ensemble averaging|ensemble]]. The quantum theory is the open Virasoro TQFT, obtained by restricting the full [[0625 Open-closed TQFT|open-closed]] Virasoro TQFT to a subclass of admissible manifolds. We show that it computes gravitational path integrals on compact regions with fixed-length boundary conditions for states above the black hole threshold, and fixed-angle boundary conditions for states below the threshold. Focusing on a special class of manifolds involving only boundary Wilson loops, we further show that the relation between [[0284 Conformal Turaev-Viro theory|Conformal Turaev-Viro theory]] and the diagonal sector of two copies of [[0596 Virasoro TQFT|Virasoro TQFT]] arises naturally from an open-closed duality.\] # Johnson, Rodrigues ## Non-perturbative data for Weil-Petersson volumes and intersection numbers using ordinary differential equations \[Links: [arXiv](https://arxiv.org/abs/2601.03351), [PDF](https://arxiv.org/pdf/2601.03351)\] \[Abstract: Recently, a new method was introduced for computing $V_{g,1}(b)$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus g with one geodesic boundary of length $b$, various supersymmetric generalizations of them, as well as analogous quantities in intersection theory. The physical setting is the computation of a certain one-point function in a variety of models of 2D gravity for which there is a double-scaled [[0197 Matrix model|random matrix model]] (RMM) description. The method combines perturbative solutions of two ordinary differential equations (ODEs), the Gel'fand-Dikii resolvent equation, and the RMM's string equation. In this paper, we extend the method to extract non-perturbative information about the $V_{g,1}(b)$ (and their analogues) that is naturally contained in the full ODEs, providing an efficient prescription for computing the transseries coefficients of the one-point correlation function, fully incorporating [[0652 ZZ brane|ZZ-brane]] and [[0658 FZZT brane|FZZT-brane]] effects, and for the first time, mixed ZZ-FZZT-effects. We use as a case study the (2,3) [[0583 Minimal string theories|minimal string]], computing perturbative and non-perturbative quantities, comparing them to perturbative results from topological recursion, and to results from the recent non-perturbative topological recursion framework of Eynard [this http URL](http://et.al/). As a particularly powerful further application we provide general predictions for the large order in g growth of $V_{g,1}(b)$, and apply them to [[0050 JT gravity|JT gravity]], finding agreement with known results, and for analogous quantities in $\mathcal{N} {=} 1$ JT supergravity, proving a conjecture of Stanford and Witten. Our predictions yield new growth formulae for the cases of $\mathcal{N} {=} 2$ and $\mathcal{N}{=}4$ JT supergravity.\] # Ju, Zhao ## The Holographic Multi-Entropy Cone \[Links: [arXiv](https://arxiv.org/abs/2606.15173), [PDF](https://arxiv.org/pdf/2606.15173)\] \[Abstract: We generalize the [[0259 Holographic entropy cone|holographic entropy cone]] (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where n includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structural conjectures: HEC facet inequalities are convex combinations of HMEC facet inequalities, and HMEC facets obey a balanced-but-not-too-balanced principle.\] # Kanda, Takayanagi, Wei ## CFT derivation of entanglement phase transition in pseudo entropy \[Links: [arXiv](https://arxiv.org/abs/2602.22994), [PDF](https://arxiv.org/pdf/2602.22994)\] \[Abstract: In this paper, we discuss the entanglement phase transition of [[0052 Pseudo-entropy|pseudo entropy]] in CFTs. We focus on the case where the in-state and the out-state are different boundary states related by boundary condition changing operators. We compute the pseudo entropy with [[0548 Boundary CFT|BCFT]] methods and find a phase transition with respect to the conformal weight of the boundary condition changing operators. For [[0001 AdS-CFT|holographic]] CFTs, we confirm that the CFT results match that evaluated in AdS.\] # Li ## Spinning States and Unitarity in 3D Gravity \[Links: [arXiv](https://arxiv.org/abs/2604.14492), [PDF](https://arxiv.org/pdf/2604.14492)\] \[Abstract: We revisit the proposal to cure the [[0678 Spectrum of 3d gravity|negative density of states]] in the three-dimensional gravitational path integral by adding spinning states whose spin scales with the [[0033 Central charge|central charge]]. We show that sub-extremal and extremal spinning states below the black hole threshold can cancel the known negativities, and interpret these states as bulk spinning defects. Additionally, certain overspinning states above the black hole threshold can cure these negativities while preserving the spectral gap. Previously interpreted as classical spinning strings, we instead identify these overspinning states with overspinning [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] geometries, which are smooth pure gravity quotients of AdS$_3$ with no fixed points. All of these spinning geometries exhibit causal pathologies in their Lorentzian continuations. Moreover, the overspinning geometries arise from mixed elliptic-hyperbolic identifications and contain a right-moving temperature and quasinormal modes. We also generalize the computation of scalar correlators to the extremal and overspinning backgrounds.\] # Liu, Ma ## Unifying soft and hard dynamics: The hard current algebra in celestial holography \[Links: [arXiv](https://arxiv.org/abs/2601.10601), [PDF](https://arxiv.org/pdf/2601.10601)\] \[Abstract: Soft current algebras capture the infrared structure of scattering in asymptotically flat spacetimes, but an analogous algebraic description of finite-energy dynamics has been missing. We uncover an infinite-dimensional hard current algebra that encodes finite-energy contributions to scattering and implies novel [[0106 Ward identity|Ward identities]]. The soft current algebras are not independent but arise naturally from the hard ones. This provides a unified algebraic framework underlying quantum theory in flat spacetime.\] # Nakayama ## To boost or not to boost, that's the question \[Links: [arXiv](https://arxiv.org/abs/2602.15275), [PDF](https://arxiv.org/pdf/2602.15275)\] \[Abstract: Or should we talk about [[0251 dS-CFT|dS/CFT]] correspondence or dS/SFT correspondence in cosmological correlators? In non-unitary field theories -- which are conjectured to be dual to cosmological correlators -- scale invariance does not necessarily imply full conformal invariance. While general relativity predicts the emergence of conformal invariance (or boost symmetry in the bulk), various modified theories of gravity suggest only scale invariance, characterized by the absence of bulk boost symmetry. We demonstrate this distinction using Einstein-Aether theory as a canonical example.\] # Pando Zayas, Zhang ## A Universality Theorem for the Quantum Thermodynamics of Near-Extremal Black Holes \[Links: [arXiv](https://arxiv.org/abs/2602.16767), [PDF](https://arxiv.org/pdf/2602.16767)\] \[Abstract: We prove that the one-loop contribution from tensor modes to the thermodynamic entropy of near-extremal black holes is universal. Our proof applies to asymptotically flat, Anti-de-Sitter and de-Sitter black holes; it also covers spherical, axial and planar symmetries. We consider black hole configurations with and without matter sectors and explicitly discuss Abelian gauge fields and neutral scalar fields with arbitrary potential. We demonstrate that under certain conditions, the thermodynamics of near-extremal black holes contains a one-loop contribution from the tensor modes that equals $\frac{3}{2}\log (T_{\rm Hawking}/T_q)$. The proof of this theorem also shows explicitly how the Schwarzian modes appear universally in near-extremal geometries in dimensions four, five and six. We apply this theorem to Kerr-de-Sitter black holes as an explicit example.\] # Sontag, Verlinde ## Baby Universe in a Coupled SYK Model \[Links: [arXiv](https://arxiv.org/abs/2605.05291), [PDF](https://arxiv.org/pdf/2605.05291)\] \[Abstract: We analyze three saddle points of the path integral computing the partition function of the [[0201 Sachdev-Ye-Kitaev model|SYK]] model with a Maldacena-Qi coupling in the double scaling limit. The three saddle points are holographically dual to three topologically different spacetimes: a pair of Euclidean black holes (two thermal disks), a thermal AdS$_2$ (a cylinder), and a thermal AdS$_2$ with a [[0051 Baby universes|baby universe]] (a cylinder with a handle). We develop explicit chord rules that span and probe these three bulk geometries. We derive the rules by expanding the effective $G,\Sigma$ action in powers of the coupling $\mathcal{J}$ and writing the partition function as a weighted sum of chord diagrams. By slicing the diagrams open, we generate a Hilbert space description on a spatial slice for each saddle point. The Hartle-Hawking chord state for the third saddle point has genuine entanglement between the baby universe and the external spacetimes, providing evidence that a [[0632 Closed universe|closed universe]] can support a nontrivial Hilbert space.\] # Wang ## Twist Operator BOPE and Entanglement Entropy in 2D Interface CFT \[Links: [arXiv](https://arxiv.org/abs/2605.01150), [PDF](https://arxiv.org/pdf/2605.01150)\] \[Abstract: We address several aspects of [[0301 Entanglement entropy|entanglement entropy]] of 2D [[0065 Defect CFT|interface CFT]] using the replica method. Unlike the case of [[0548 Boundary CFT|boundary CFT]], we consider the boundary OPE (BOPE) of the Rényi twist operator and find a boundary twist operator anchored on the interface. This approach gives the $O(1)$ contribution to the entanglement entropy in terms of the BOPE coefficients of the twist operator. We further analyze entanglement entropy of different intervals and compare our findings with previous holographic results.\]