Exact thermal correlators at vanishing momenta and the black hole singularity

Abstract

We study thermal two- and three-point functions of scalar primaries in holographic CFTs dual to AdS black branes. The three-point function arises from a cubic scalar interaction in the bulk. At vanishing external momenta, the tree-level results can be written in closed form and are exact in the operator dimensions. We reproduce them through direct CFT calculations in two dimensions. Their large-dimension expansions contain subleading exponential terms encoding the radial proper time from the horizon to the black hole singularity. These results provide an exact test of earlier WKB and saddle-point predictions for higher-point thermal correlators, confirming the proper-time signature while correcting the predicted asymptotic form.