The Regge limit of AdS$_3$ holographic correlators

TL;DR

This paper investigates the behavior of 4-point correlators in AdS$_3$ holography within the Regge limit, connecting bulk eikonal phases to boundary operator dimensions, and distinguishes between different heavy state geometries.

Contribution

It provides explicit checks of the relation between bulk eikonal phases and boundary anomalous dimensions, and analyzes the impact of heavy operator states on the Regge limit in AdS$_3$/CFT$_2$.

Findings

Bulk eikonal phase relates to anomalous dimensions of double-trace operators.

Heavy operators with conformal dimension proportional to central charge influence correlator behavior.

Minimal solutions for conical defect geometries differ from microstate geometry solutions.

Abstract

We study the Regge limit of 4-point AdS$_3 \times S^3$ correlators in the tree-level supergravity approximation and provide various explicit checks of the relation between the eikonal phase derived in the bulk picture and the anomalous dimensions of certain double-trace operators. We consider both correlators involving all light operators and HHLL correlators with two light and two heavy multi-particle states. These heavy operators have a conformal dimension proportional to the central charge and are pure states of the theory, dual to asymptotically AdS$_3 \times S^3$ regular geometries. Deviation from AdS$_3 \times S^3$ is parametrised by a scale $\mu$ and is related to the conformal dimension of the dual heavy operator. In the HHLL case, we work at leading order in $\mu$ and derive the CFT data relevant to the bootstrap relations in the Regge limit. Specifically, we show that the minimal solution to these equations relevant for the conical defect geometries is different to the solution implied by the microstate geometries dual to pure states.