OPE statistics from higher-point crossing

TL;DR

This paper derives new asymptotic formulas for the distribution of OPE coefficients in conformal field theories, revealing non-Gaussian features and providing the first such constraints for heavy-heavy-heavy interactions in higher dimensions.

Contribution

It introduces the first asymptotic formulas constraining heavy-heavy-heavy OPE coefficients in dimensions greater than two, based on crossing symmetry of higher-point functions.

Findings

Derived asymptotic formulas for OPE coefficient distributions

Identified non-Gaussianities in OPE coefficient statistics

Provided refined formulas for 2D CFTs involving Virasoro primaries

Abstract

We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions. They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients. We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension. This is the first asymptotic formula constraining heavy-heavy-heavy OPE coefficients in $d>2$. For two-dimensional CFTs, we present refined asymptotic formulas stemming from exchanges of quasi-primaries as well as Virasoro primaries.