Thermal Double-Twist Data in Holography

Abstract

We explain how to extract thermal OPE coefficients of double-twist operators in scalar two-point functions at infinite spatial volume from suitably regularized integrals of thermal response functions in momentum space. As a specific application, we implement the proposed approach to four-dimensional holographic CFTs with an Einstein bulk action, where the finite-temperature state is captured by an AdS$_5$ black-brane geometry. In that case, the thermal response function can be computed on the gravitational side by solving numerically a radial ODE reduction of the Klein-Gordon equation. We obtain accurate values of double-twist data from this solution, completing previous holographic and bootstrap studies of thermal two-point functions. Some of the reported spin-resolved data that we compute are new.