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arXiv · 2112.09143

OPE statistics from higher-point crossing

Tarek Anous·Alexandre Belin·Jan de Boer·Diego Liska
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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.

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Tarek Anous, Alexandre Belin, Jan de Boer, Diego Liska. 2021-12-16. OPE statistics from higher-point crossing. https://doi.org/10.1007/jhep06(2022)102

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