Thermal AdS two-point functions and loop induced effective one-point vertices

Abstract

We present a study of thermal two-point functions from Witten diagrams in thermal AdS$_{d+1}$, defined with the conformal boundary $S_β^1 \times \mathbb{R}^{d-1}$, with an aim to establish a connection between thermal CFT data and perturbative bulk dynamics. We analyze one-loop tadpole and bench diagrams arising from the cubic $ϕϕχ$ interaction in the bulk, segregating the different relative thermal winding sectors for the bench, and also extend the analysis to include quartic scalar contact diagrams with and without derivative interactions. We also analyze the spinning exchange thermal two-point function. Utilizing the split representation of bulk propagators and the method of images we reorganize the thermal Witten diagrams into the standard AdS integrals and obtain spectral and image-sum representations that make KMS periodicity of the correlators manifest. Additionally, we show possible position dependent effective one-point vertices of scalar and spinning fields in the bulk arising from the reduction of the coincident- point thermal bulk to bulk propagator loop, allowing tadpole-type diagrams to be reconstructed from effective local bulk interactions. The bench diagram however retains an intrinsically bi-local structure. We further investigate the thermal one-point coefficients and perturbative OPE data encoded in these thermal correlators, including contributions associated with anomalous dimensions. Finally, we examine their relation to thermal dispersion relations and the role of contributions that are not determined by discontinuity data alone. Our results provide a set of explicit bulk constructions for exploring the analytic structure of thermal CFT correlators and their connection to the thermal conformal bootstrap.