Holographic Correlators at Finite Temperature

TL;DR

This paper computes holographic thermal two-point functions of scalar operators in finite-temperature AdS, providing analytic corrections for local quartic interactions and establishing a dispersion relation for these correlators.

Contribution

It introduces a method to analytically compute finite-temperature holographic correlators with local interactions and derives a dispersion relation for thermal two-point functions.

Findings

Analytic expressions for corrections due to local quartic interactions.

Agreement with diagrammatic computations for the non-derivative case.

Proposal of a thermal Mellin amplitude structure.

Abstract

We consider weakly-coupled QFT in AdS at finite temperature. We compute the holographic thermal two-point function of scalar operators in the boundary theory. We present analytic expressions for leading corrections due to local quartic interactions in the bulk, with an arbitrary number of derivatives and for any number of spacetime dimensions. The solutions are fixed by judiciously picking an ansatz and imposing consistency conditions. The conditions include analyticity properties, consistency with the operator product expansion, and the Kubo-Martin-Schwinger condition. For the case without any derivatives we show agreement with an explicit diagrammatic computation. The structure of the answer is suggestive of a thermal Mellin amplitude. Additionally, we derive a simple dispersion relation for thermal two-point functions which reconstructs the function from its discontinuity.