Exact holographic thermal spectral functions: OPE, non-perturbative corrections, and black hole singularity

Original Abstract

We study analytic properties of thermal spectral functions of holographic CFTs, examining both their (a) exact properties at finite momentum and (b) asymptotics at large momentum. For even-dimensional holographic CFTs on Minkowski spacetime and for scalar primaries with integer dimensions, we demonstrate that the exact spectral function at finite momentum factorizes into a perturbative/OPE piece and a non-perturbative piece. The former is controlled by stress tensor exchange and fixed by a near-boundary analysis. The latter encodes information about the bulk interior, including the black hole horizon and singularity. Utilizing the exact factorization, we obtain the full transseries expansion of the non-perturbative piece at large timelike momentum. This is achieved by employing exact WKB techniques to compute the monodromy of the bulk wave equation. Finally, we use these results to work out the singular loci of a spatially averaged thermofield double correlator in the complex time plane. These singular loci have been argued to provide imprints of the black hole curvature singularity in the dual CFT observables. Our result, which includes the case of non-vanishing momentum, gives a clear link between the non-perturbative spectral function and the black hole singularity.