Analytic thermal bootstrap meets holography

Abstract: We compute thermal holographic correlators by combining their analytic structure with the Kubo-Martin-Schwinger (KMS) condition and a finite set of multi-stress tensor OPE coefficients determined from the dual AdS description. We focus on two-point functions of identical scalar operators with integer conformal dimensions at zero spatial separation. For correlators holographically dual to black brane backgrounds, we show that our results satisfy all relevant consistency conditions and agree with numerical solutions of the bulk wave equation. We further demonstrate that the expansion in generalized free field correlators proposed in [Barrat,6/2025] admits a natural interpretation in terms of Witten diagrams. Finally, we extend our analysis to spherically symmetric black hole backgrounds and show that higher-curvature corrections can be incorporated within the same framework.