Non-Gaussianities in the statistical distribution of heavy OPE coefficients and wormholes

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