Holographic thermal correlators revisited

TL;DR

This paper analyzes holographic 2-point correlators for scalar operators with large conformal dimensions, incorporating bulk cubic and higher curvature couplings, revealing corrections related to interior black hole structure and operator mixing.

Contribution

It introduces a method to compute first-order corrections to holographic correlators including higher curvature effects and bulk interactions, extending previous geodesic approximation results.

Findings

Correction terms proportional to VEV of neutral operators

Matching of correction form with conformal field theory expectations

Leading contribution to off-diagonal correlators computed holographically

Abstract

We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator $O_k$ and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of $T^nO_k$ (being $T^n$ the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.