The Regge limit of AdS$_3$ holographic correlators with heavy states: towards the black hole regime

TL;DR

This paper investigates the Regge limit of holographic 4-point functions in AdS3 involving heavy and light operators, deriving all-order relations between phase shifts and OPE data, with applications to conical defects and black hole microstates.

Contribution

It extends previous work by deriving all-order relations between bulk phase shifts and Regge limit OPE data for heavy-light correlators in AdS3, beyond low-order approximations.

Findings

Derived all-order relations between phase shifts and OPE data.

Analyzed correlators for conical defect geometries and black hole microstates.

Validated results with explicit examples of known correlators.

Abstract

We examine the Regge limit of holographic 4-point correlation functions in AdS$_3\times S^3$ involving two heavy and two light operators. In this kinematic regime such correlators can be reconstructed from the bulk phase shift accumulated by the light probe as it traverses the geometry dual to the heavy operator. We work perturbatively -- but to arbitrary orders -- in the ratio of the heavy operator's conformal dimension to the dual CFT${}_2$'s central charge, thus going beyond the low order results of arXiv:1812.03120 and arXiv:2007.12118. In doing so, we derive all-order relations between the bulk phase shift and the Regge limit OPE data of a class of heavy-light multi-trace operators exchanged in the cross-channel. Furthermore, we analyse two examples for which the relevant 4-point correlators are known explicitly to all orders: firstly the case of heavy operators dual to AdS${}_3$ conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.