Holographic correlators at finite temperature

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