The Effects of Near-AdS$_2$ Backreaction on Matter Fields

We quantify how the two-point function of a real scalar field is affected by the distortion caused by deforming AdS$_2$ to a near-AdS$_2$ background. At tree-level, the backreaction of the geometry induces a finite-temperature correction to the correlator that arises from interactions that the background generates. For a massive field, we show that this correction is not captured by JT gravity coupled to matter: it requires a backreaction of the metric field. For a massless field, the correction is controlled solely by the dilaton and hence is model-independent. We compare our findings with correlation functions on BTZ and find perfect agreement. We use our results to quantify the corrections for a class of correlators relevant to five- and four-dimensional black holes. We discuss how these corrections would enter in a holographic description of near-AdS$_2$; we also comment on how these corrections provide a universal prediction for quasinormal modes in higher dimensions.