ETH and Modular Invariance of 2D CFTs

TL;DR

This paper investigates the properties of three-point functions in 2D conformal field theories using modular invariance, demonstrating consistency with ETH and exploring open-closed duality and disk one-point functions.

Contribution

It introduces a novel analysis of heavy-light-heavy three-point functions via modular invariance and connects these results with ETH and open-closed duality in 2D CFTs.

Findings

Consistency of three-point functions with ETH

Behavior of disk one-point functions derived

Insights into open-closed duality in 2D CFTs

Abstract

We study properties of heavy-light-heavy three-point functions in two-dimensional CFTs by using the modular invariance of two-point functions on a torus. We show that our result is non-trivially consistent with the condition of ETH (Eigenstate Thermalization Hypothesis). We also study the open-closed duality of cylinder amplitudes and derive behaviors of disk one-point functions.