Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories

We study properties of heavy-light-heavy three-point functions in two-dimensional conformal field theories by using the modular invariance of two-point functions on a torus. We show that the result is nontrivially consistent with the condition of eigenstate thermalization hypothesis. We also study the open-closed duality of cylinder amplitudes and derive behaviors of disk one-point functions.