OPE statistics from higher-point crossing

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.

30 pages + appendices, 7 figures; v2 references and footnotes added

References in corpus (8)

• A tauberian theorem for the conformal bootstrap
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Charged structure constants from modularity
• Phases of scrambling in eigenstates
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• Lightcone Bootstrap at higher points
• Product of Random States and Spatial (Half-)Wormholes

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• Multiboundary wormholes and OPE statistics
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