# A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance

## TL;DR

This paper derives a universal asymptotic formula for three-point operator product expansion coefficients in 2D conformal field theories, utilizing genus two modular invariance and monodromy techniques at large central charge.

## Contribution

It generalizes the asymptotic density of states formula to three-point coefficients using genus two modular invariance and computes conformal block asymptotics explicitly.

## Key findings

- Derived a universal asymptotic formula for OPE coefficients.
- Connected genus two modular invariance to OPE asymptotics.
- Computed conformal block asymptotics at large central charge.

## Abstract

We derive an asymptotic formula for operator product expansion coefficients of heavy operators in two dimensional conformal field theory. This follows from modular invariance of the genus two partition function, and generalises the asymptotic formula for the density of states from torus modular invariance. The resulting formula is universal, depending only on the central charge, but involves the asymptotic behaviour of genus two conformal blocks. We use monodromy techniques to compute the asymptotics of the relevant blocks at large central charge to determine the behaviour explicitly.