Random Statistics of OPE Coefficients and Euclidean Wormholes

Abstract

We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the Eigenstate Thermalization Hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS${}_3$, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.

7 pages, 3 figures; v2, minor comments and references added, version as appearing in CQG

References in corpus (9)

• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• JT gravity as a matrix integral
• AdS${}_3$ gravity and random CFT
• Eigenstate Thermalization and Disorder Averaging in Gravity
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Heavy Operators and Hydrodynamic Tails
• Phases of scrambling in eigenstates
• Constraining CP-violating electron-gluonic operators

Cited by in corpus (84)

• Semiclassical 3D gravity as an average of large-c CFTs
• Free Energy from Replica Wormholes
• Summing over Geometries in String Theory
• More quantum noise from wormholes
• Solving 3d Gravity with Virasoro TQFT
• Euclidean wormhole in the SYK model
• The Virasoro Minimal String
• Wormholes and black hole microstates in AdS/CFT
• Gravitational Constrained Instantons
• Spin Impurities, Wilson Lines and Semiclassics
• Gravity factorized
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Gravitational orbits, double-twist mirage, and many-body scars
• Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
• Wormholes & Holography: An Introduction
• OPE statistics from higher-point crossing
• Wormholes and Spectral Statistics in the Narain Ensemble
• From operator statistics to wormholes
• Wormholes without averaging
• Comments on the holographic description of Narain theories
• Wormholes from heavy operator statistics in AdS/CFT
• Ensemble from Coarse Graining: Reconstructing the Interior of an Evaporating Black Hole
• Interacting systems and wormholes
• A principle of maximum ignorance for semiclassical gravity
• A universe field theory for JT gravity
• Islands with Gravitating Baths: Towards ER = EPR
• Alpha states demystified: Towards microscopic models of AdS${}_2$ holography
• Thermalization in Large-N CFTs
• Homology Conditions for RT Surfaces in Double Holography
• Generalized Spectral Form Factors and the Statistics of Heavy Operators
• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Toward random tensor networks and holographic codes in CFT
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Holographic Quantum Scars
• Multiboundary wormholes and OPE statistics
• A precision test of averaging in AdS/CFT
• A microscopic realization of dS${}_3$
• Half-wormholes in nearly AdS${}_2$ holography
• The OPE meets semiclassics
• Seeing behind black hole horizons in SYK
• Holevo Information and Ensemble Theory of Gravity
• Large Charge Sector of 3d Parity-Violating CFTs
• Holographic boundary actions in AdS${}_3$/CFT${}_2$ revisited
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Baby Universes and Worldline Field Theories
• Entanglement island, miracle operators and the firewall
• Microstructure in matrix elements
• Comments on wormholes and factorization
• Wormholes in Quantum Mechanics
• Quantum Chaos on Edge
• 3d Gravity as a random ensemble
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Semiclassical Gravity from Averaged Boundaries in two-dimensional BCFTs
• Integrality, Duality and Finiteness in Combinatoric Topological Strings
• Wormholes from Averaging over States
• From the Black Hole Conundrum to the Structure of Quantum Gravity
• Gravity without averaging
• Complexity via Replica Trick
• Higher spin JT gravity and a matrix model dual
• Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos
• On the saturation of late-time growth of complexity in supersymmetric JT gravity
• Ensemble averages, Poisson processes and Microstates
• Ergodic Equilibration of Rényi Entropies and Replica Wormholes
• Wormholes with Ends of the World
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Chaotic and Thermal Aspects in the Highly Excited String S-Matrix
• The entanglement entropy of typical pure states and replica wormholes
• D-branes and Orbit Average
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• Entanglement Properties of SU(2) Gauge Theory
• A Tale of Two Saddles
• Random Circuits in the Black Hole Interior
• Baby universes, ensemble averages and factorizations with matters
• Product of Random States and Spatial (Half-)Wormholes
• Open-closed 3d gravity as a random ensemble
• Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators
• A Reverse Black Hole Information Problem
• A universal sum over topologies in 3d gravity
• Replicas, averaging and factorization in the IIB matrix model
• Factorization and global symmetries in holography
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity