arXiv subjects

Kyriakos Papadodimas

Publications and source records attributed to Kyriakos Papadodimas.

At least 19 recordsLinked to original sources

arXiv2026

Chaos of Berry curvature for BPS microstates

We expect black hole microstates to differ in their chaotic properties from states associated with other geometries. For supersymmetric black holes, ordinary level statistics cannot diagnose this distinction, since their energy levels are exactly degenerate. We propose that there is an intrinsic probe of chaos, encoded in the mixing of the microstates under changes in the couplings of the theory, as determined by the non-Abelian Berry curvature of the BPS states under certain deformations. For states dual to horizonless geometries in holographic systems, such as 1/2-BPS states in the D1/D5 CFT and 1/4-BPS states in $\mathcal{N}=4$ SYM, we find that the Berry curvature for marginal deformations is non-random and often exactly zero at generic couplings. By contrast, for states dual to supersymmetric black holes, we show through computations in $\mathcal{N}=2$ super-JT gravity and explicit numerics in the $\mathcal{N}=2$ SYK model that the Berry curvature resembles a random matrix. We also uncover interesting topological features of the $\mathcal{N}=2$ SYK moduli space, as probed by Chern numbers. These results suggest that the Berry curvature sharply distinguishes black hole microstates from smooth horizonless states and provides a robust diagnostic of chaos in supersymmetric sectors.

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arXiv2026

A 1/4-BPS chiral algebra in D1D5: from charge concentration to BPS chaos

The D1D5 CFT exhibits a charge concentration puzzle for BPS states, similar to, but simpler than, that of $\mathcal{N}=4$ SYM. We consider the chiral algebra of 1/4-BPS operators in the D1D5 CFT arising from a supercharge cohomology, and the resulting rational correlators. Using crossing symmetry and this chiral algebra, we establish a non-perturbative proof of the existence of a family of 1/4-BPS states away from the charge concentration locus for general coupling and finite central charge. We further discuss possible implications for BPS chaos in the D1D5 CFT and compute a late-time BPS plateau at the orbifold point.

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arXiv2026

BPS Non-Renormalization in the BMN Matrix Model

We show in the $(0+1)$-dimensional Berenstein-Maldacena-Nastase matrix model, dual to M-theory on a pp-wave background, that the coupling can be changed between any two finite, non-zero values using a special class of deformations, known as conjugation deformations. Importantly, we prove that they preserve normalizability of the states. This implies that BPS states in the model cannot lift as the couplings are varied, and hence their (unsigned) number cannot change, except at the free point and Banks-Fischler-Shenker-Susskind point.

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arXiv2024

Holography and Localization of Information in Quantum Gravity

Within the AdS/CFT correspondence, we identify a class of CFT operators which represent diff-invariant and approximately local observables in the gravitational dual. Provided that the bulk state breaks all asymptotic symmetries, we show that these operators commute to all orders in $1/N$ with asymptotic charges, thus resolving an apparent tension between locality in perturbative quantum gravity and the gravitational Gauss law. The interpretation of these observables is that they are not gravitationally dressed with respect to the boundary, but instead to features of the state. We also provide evidence that there are bulk observables whose commutator vanishes to all orders in $1/N$ with the entire algebra of single-trace operators defined in a space-like separated time-band. This implies that in a large $N$ holographic CFT, the algebra generated by single-trace operators in a short-enough time-band has a non-trivial commutant when acting on states which break the symmetries. It also implies that information deep in the interior of the bulk is invisible to single-trace correlators in the time-band and hence that it is possible to localize information in perturbative quantum gravity.

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arXiv2023

State-dressed local operators in the AdS/CFT correspondence

We examine aspects of locality in perturbative quantum gravity and how information can be localized in subregions. In the framework of AdS/CFT, we consider the algebra of single-trace operators defined in a short time band. We conjecture that, if the state has large energy variance, then this algebra will have a commutant in the 1/N expansion. We provide evidence for this by identifying operators that commute with the conformal field theory Hamiltonian to all orders in 1/N, thus resolving an apparent tension with the gravitational Gauss law. The bulk interpretation is that these operators are gravitationally dressed with respect to features of the state rather than the boundary. We comment on observables in certain black hole microstates and the gravitational dressing in the island proposal.

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arXiv2022

Frontiers of Quantum Gravity: shared challenges, converging directions

Understanding the quantum nature of spacetime and gravity remains one of the most ambitious goals of theoretical physics. It promises to provide key new insights into fundamental particle theory, astrophysics, cosmology and the foundations of physics. Despite this common goal, the community of quantum gravity researchers is sometimes seen as divided into sub-communities working on different, mutually exclusive approaches. In practice however, recent years have shown the emergence of common techniques, results and physical ideas arising from different sub-communities, suggesting exciting new prospects for collaboration and interaction between traditionally distinct approaches. In this White Paper we discuss some of the common themes which have seen a growing interest from various directions, and argue that focusing on them will help the quantum gravity community as a whole towards shared objectives.

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arXiv2021

On the Kähler-Hodge structure of superconformal manifolds

We show that conformal manifolds in $d\geq 3$ conformal field theories with at least 4 supercharges are Kähler-Hodge, thus extending to 3d ${\cal N}=2$ and 4d ${\cal N}=1$ similar results previously derived for 4d ${\cal N}=2$ and ${\cal N}=4$ and various types of 2d SCFTs. Conformal manifolds in SCFTs are equipped with a holomorphic line bundle ${\cal L}$, which encodes the operator mixing of supercharges under marginal deformations. Using conformal perturbation theory and superconformal Ward identities, we compute the curvature of ${\cal L}$ at a generic point on the conformal manifold. We show that the Kähler form of the Zamolodchikov metric is proportional to the first Chern class of ${\cal L}$, with a constant of proportionality given by the two-point function coefficient of the stress tensor, $C_T$. In cases where certain additional conditions about the nature of singular points on the conformal manifold hold, this implies a quantization condition for the total volume of the conformal manifold.

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arXiv2019

A simple quantum test for smooth horizons

We develop a new test that provides a necessary condition for a quantum state to be smooth in the vicinity of a null surface: near-horizon modes that can be defined locally near any patch of the null surface must be correctly entangled with each other and with their counterparts across the surface. This test is considerably simpler to implement than a full computation of the renormalized stress-energy tensor. We apply this test to Reissner-Nordstrom black holes in asymptotically anti-de Sitter space and provide numerical evidence that the inner horizon of such black holes is singular in the Hartle-Hawking state. We then consider BTZ black holes, where we show that our criterion for smoothness is satisfied as one approaches the inner horizon from outside. This results from a remarkable conspiracy between the properties of mode-functions outside the outer horizon and between the inner and outer horizon. Moreover, we consider the extension of spacetime across the inner horizon of BTZ black holes and show that it is possible to define modes behind the inner horizon that are correctly entangled with modes in front of the inner horizon. Although this provides additional suggestions for the failure of strong cosmic censorship, we lay out several puzzles that must be resolved before concluding that the inner horizon will be traversable.

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arXiv2019

A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta

We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of these correlators is bounded by $e^{-βR}$, where $R$ is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in $d$-spacetime dimensions, where we show that the leading two-point function of generalized free-fields saturates the bound in $d = 2$ and is below the bound for $d > 2$. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

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arXiv2019

Probing typical black hole microstates

We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturbations of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.

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arXiv2018

On the interior geometry of a typical black hole microstate

We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form ${\cal O} \widetilde{\cal O}$, where $\widetilde{\cal O}$ denote the state-dependent "mirror operators". We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.

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arXiv2017

Quantum teleportation through time-shifted AdS wormholes

Based on the work of Gao-Jafferis-Wall and Maldacena-Stanford-Yang, we observe that the time-shifted thermofield states of two entangled CFTs can be made traversable by an appropriate coupling of the two CFTs, or alternatively by the application of a modified quantum teleportation protocol. This provides evidence for the smoothness of the horizon for a large class of entangled states related to the thermofield by time-translations. The smoothness of these states has some relevance for the firewall paradox and the proposal that some observables in quantum gravity may be state-dependent. We notice that quantum teleportation through these entangled states could be used in a laboratory setup to implement a time-machine, which allows the observer to travel far in the future.

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arXiv2017

A class of non-equilibrium states and the black hole interior

We consider a class of non-equilibrium pure states, which are generally present in an isolated quantum statistical system. These are states of the form $|Ψ\rangle=e^{-{βH \over 2}} U e^{βH \over 2} |Ψ_0\rangle$, where $U$ is a unitary made out of simple operators and $|Ψ_0\rangle$ is a typical equilibrium pure state with sharply peaked energy. We argue that in a system with a holographic dual these states have a natural interpretation as an AdS black hole with transient excitations behind the horizon. We explore the interpretation of these states as pure states undergoing a time-dependent spontaneous fluctuation out of equilibrium. While these states are atypical and the microscopic phases of the wavefunction are correlated with the matrix elements of simple operators, the states are partly disguised as equilibrium states due to cancellations between contributions from different coarse-grained energy bins. These cancellations are guaranteed by the KMS condition of the underlying equilibrium state $|Ψ_0\rangle$. However, in correlators which include the Hamiltonian $H$ these cancellations are spoiled and the non-equilibrium nature of the state $|Ψ\rangle$ can be detected. We discuss connections with the proposal that local observables behind the horizon are realized as state-dependent operators. The states studied in this paper may be useful for implementing an analogue of the "traversable wormhole" protocol for a 1-sided black hole, which could potentially allow us to extract the excitation from behind the horizon. We include some pedagogical background material.

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arXiv2017

Aspects of Berry phase in QFT

When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing---a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We also argue that a large class of QFTs with rich Berry properties is provided by CFTs with non-trivial conformal manifolds. Using the operator-state correspondence we demonstrate in this case that the Berry connection is equivalent to the connection on the conformal manifold derived previously in conformal perturbation theory. In the special case of chiral primary states in 2d N=(2,2) and 4d N=2 SCFTs the Berry phase is governed by the tt* equations. We present a technically useful rederivation of these equations using quantum mechanics methods.

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arXiv2016

Large-N correlation functions in ${\cal N} = 2$ superconformal QCD

We study extremal correlation functions of chiral primary operators in the large-N SU(N) ${\cal N} = 2$ superconformal QCD theory and present new results based on supersymmetric localization. We discuss extensively the basis-independent data that can be extracted from these correlators using the leading order large-N matrix model free energy given by the four-sphere partition function. Special emphasis is given to single-trace 2- and 3-point functions as well as a new class of observables that are scalars on the conformal manifold. These new observables are particular quadratic combinations of the structure constants of the chiral ring. At weak 't Hooft coupling we present perturbative results that, in principle, can be extended to arbitrarily high order. We obtain closed-form expressions up to the first subleading order. At strong coupling we provide analogous results based on an approximate Wiener-Hopf method.

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arXiv2016

A toy model of black hole complementarity

We consider the algebra of simple operators defined in a time band in a CFT with a holographic dual. When the band is smaller than the light crossing time of AdS, an entire causal diamond in the center of AdS is separated from the band by a horizon. We show that this algebra obeys a version of the Reeh-Schlieder theorem: the action of the algebra on the CFT vacuum can approximate any low energy state in the CFT arbitrarily well, but no operator within the algebra can exactly annihilate the vacuum. We show how to relate local excitations in the complement of the central diamond to simple operators in the band. Local excitations within the diamond are invisible to the algebra of simple operators in the band by causality, but can be related to complicated operators called "precursors". We use the Reeh-Schlieder theorem to write down a simple and explicit formula for these precursors on the boundary. We comment on the implications of our results for black hole complementarity and the emergence of bulk locality from the boundary.

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arXiv2015

On exact correlation functions in SU(N) ${\cal N} = 2$ superconformal QCD

We consider the exact coupling constant dependence of extremal correlation functions of ${\cal N} = 2$ chiral primary operators in 4d ${\cal N} = 2$ superconformal gauge theories with gauge group SU(N) and N_f=2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt* equations. In the case at hand, the tt* equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equations to a sequence of decoupled semi-infinite Toda chains, similar to the one encountered previously in the special case of SU(2) gauge group. This ansatz requires a surprising new non-renormalization theorem in ${\cal N} = 2$ superconformal field theories. We derive a general 3-loop perturbative formula for 2- and 3-point functions in the ${\cal N} = 2$ chiral ring of the SU(N) theory, and in all explicitly computed examples we find agreement with the tt* equations, as well as the above-mentioned ansatz. This is suggestive evidence for an interesting non-perturbative conjecture about the structure of the ${\cal N} = 2$ chiral ring in this class of theories. We discuss several implications of this conjecture. For example, it implies that the holonomy of the vector bundles of chiral primaries over the superconformal manifold is reducible. It also implies that a specific subset of extremal correlation functions can be computed in the SU(N) theory using information solely from the S^4 partition function of the theory obtained by supersymmetric localization.

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arXiv2015

Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior

We revisit the "state-dependence" of the map that we proposed recently between bulk operators in the interior of a large AdS black hole and operators in the boundary CFT. By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon --- not only for single-sided black holes but even in the eternal black hole. We show that state-dependence is invisible to an infalling observer who cannot differentiate these operators from those of ordinary quantum effective field theory. Therefore the infalling observer does not observe any violations of quantum mechanics. We successfully resolve a large class of potential ambiguities in our construction. We analyze states where the CFT is entangled with another system and show that the ER=EPR conjecture emerges from our construction in a natural and precise form. We comment on the possible semi-classical origins of state-dependence.

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