Random Statistics of OPE Coefficients and Euclidean Wormholes

TL;DR

This paper introduces a Gaussian random variable model for OPE coefficients in chaotic CFTs, linking their statistical properties to Euclidean wormholes in AdS$_3$ and explaining non-factorization phenomena.

Contribution

It generalizes the Eigenstate Thermalization Hypothesis to OPE coefficients, enabling computation of higher moments and connecting OPE statistics to gravitational wormholes.

Findings

The ansatz reproduces non-perturbative wormhole corrections.

It explains the non-factorization of partition function products.

Provides a physical interpretation of OPE coefficient randomness.

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.