Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes

Abstract

The Eigenstate Thermalization Hypothesis makes a prediction for the statistical distribution of matrix elements of simple operators in energy eigenstates of chaotic quantum systems. As a leading approximation, off-diagonal matrix elements are described by Gaussian random variables but higher-point correlation functions enforce non-Gaussian corrections which are further exponentially suppressed in the entropy. In this paper, we investigate non-Gaussian corrections to the statistical distribution of heavy-heavy-heavy OPE coefficients in chaotic two-dimensional conformal field theories. Using the Virasoro crossing kernels, we provide asymptotic formulas involving arbitrary numbers of OPE coefficients from modular invariance on genus-$g$ surfaces. We find that the non-Gaussianities are further exponentially suppressed in the entropy, much like the ETH. We discuss the implication of these results for products of CFT partition functions in gravity and Euclidean wormholes. Our results suggest that there are new connected wormhole geometries that dominate over the genus-two wormhole.

30 pages + appendices, 13 figures; v3 references and notes added

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• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Generalized Spectral Form Factors and the Statistics of Heavy Operators
• Toward random tensor networks and holographic codes in CFT
• Holographic Quantum Scars
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• A precision test of averaging in AdS/CFT
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• 3d Gravity as a random ensemble
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• Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
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• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• A universal sum over topologies in 3d gravity
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