Modular crossings, OPE coefficients and black holes

TL;DR

This paper leverages modular symmetry in 2D conformal field theories to derive a universal formula for operator product expansion coefficients involving heavy primaries, connecting CFT data to black hole physics.

Contribution

It introduces a novel approach using modular properties to obtain asymptotic OPE coefficients involving heavy operators, linking CFT correlators to gravitational black hole features.

Findings

Derived a universal asymptotic formula for OPE coefficients with heavy primaries.

Connected CFT crossing symmetry to gravitational 2-to-2 S-matrix features.

Revealed black hole signatures in the coarse-grained heavy channel analysis.

Abstract

In (1+1)-d CFTs, the 4-point function on the plane can be mapped to the pillow geometry and thereby crossing symmetry gets translated into a modular property. We use these modular features to derive a universal asymptotic formula for OPE coefficients in which one of the operators is averaged over heavy primaries. The coarse-grained heavy channel then reproduces features of the gravitational 2-to-2 S-matrix which has black holes as their intermediate states.