Multiboundary wormholes and OPE statistics

TL;DR

This paper connects the statistical distribution of OPE coefficients in holographic 2D CFTs to multiboundary wormholes in 3D gravity, deriving universal moments and proposing a fixed ensemble based on symmetry principles.

Contribution

It derives universal higher moments of OPE coefficients, relates them to multiboundary wormholes, and conjectures a fixed statistical ensemble based on crossing symmetry and modular invariance.

Findings

Universal cubic and quartic moments match entropy scaling.

Connected averages correspond to new multiboundary wormhole topologies.

Heavy operator statistics depend on light spectrum, interpreted via Wilson loops.

Abstract

We derive higher moments in the statistical distribution of OPE coefficients in holographic 2D CFTs, and show that such moments correspond to multiboundary Euclidean wormholes in pure 3D gravity. The n-th cyclic non-Gaussian contraction of heavy-heavy-light OPE coefficients follows from crossing symmetry of the thermal n-point function. We derive universal expressions for the cubic and quartic moments and demonstrate that their scaling with the microcanonical entropy agrees with a generalization of the Eigenstate Thermalization Hypothesis. Motivated by this result, we conjecture that the full statistical ensemble of OPE data is fixed by three premises: typicality, crossing symmetry and modular invariance. Together, these properties give predictions for non-factorizing observables, such as the generalized spectral form factor. Using the Virasoro TQFT, we match these connected averages to new on-shell wormhole topologies with multiple boundary components. Lastly, we study and clarify examples where the statistics of heavy operators are not universal and depend on the light operator spectrum. We give a gravitational interpretation to these corrections in terms of Wilson loops winding around non-trivial cycles in the bulk.