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

TL;DR

This paper studies the non-Gaussian statistical distribution of heavy OPE coefficients in chaotic conformal field theories, revealing exponential suppression of non-Gaussianities and implications for wormhole geometries in gravity.

Contribution

It provides asymptotic formulas for non-Gaussian corrections to OPE coefficients using Virasoro crossing kernels and explores their implications for wormhole dominance in gravity.

Findings

Non-Gaussianities are exponentially suppressed in entropy.

New connected wormhole geometries may dominate over genus-two wormholes.

Asymptotic formulas involve arbitrary numbers of OPE coefficients.

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.