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.
Highlights
The dynamics exactly solvable, such as integrability or supersymmetry.2 Because of this having some exactly solvable examples of thermal observables in QFTs can potentially be very useful
We propose the general answer for the thermal two-point functions corresponding to quartic interactions with derivatives
In this paper we have presented an infinite number of corrections to the mean field theory (MFT) thermal twopoint function, corresponding to quartic vertices in the bulk with an arbitrary number of derivatives
Summary
The thermal bootstrap as developed in [8, 11] systematically solves for thermal coefficients by imposing the consistency of overlapping OPE channels, with the KMS condition as a crossing equation Another useful tool in this context is a thermal Lorentzian inversion formula (TLIF). Analogous to the Lorentzian inversion formula for T = 0 four-point functions [12], the TLIF decomposes the thermal two-point function into the OPE data with manifest analyticity in the spin, J, of constituent operators.. Analogous to the Lorentzian inversion formula for T = 0 four-point functions [12], the TLIF decomposes the thermal two-point function into the OPE data with manifest analyticity in the spin, J, of constituent operators.4 Another useful set of variables that we frequently use are defined as follows. The functions describing the MFT data are analytic functions of n, and we will use this property.
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