Analyticity of replica correlators and modular ETH

A bstract We study the two point correlation function of a local operator on an n -sheeted replica manifold corresponding to half-space in vacuum state conformal field theory. In analogy with inverse Laplace transform, we define Renyi transform this function, which is one complex variable w , dual parameter . Inspired by inversion formula Caron-Huot, argue that if f ( ) has bounded behavior at infinity plane, discontinuity disc provides unique analytic continuation original function. check our explicitly calculating particular correlator large N holographic CFT d dimensions > 2. also discover related matrix element operators between distinct eigenstates modular Hamiltonian. calculate 2 theories, and use it extract off-diagonal elements (modular) ETH. equivalent OPE coefficients show technique exactly reproduces recent results literature.