The Regge limit of AdS3 holographic correlators

Abstract

We study the Regge limit of 4-point AdS3× S3 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 AdS3× S3 regular geometries. Deviation from AdS3× S3 is parametrised by a scale μ and is related to the conformal dimension of the dual heavy operator. In the HHLL case, we work at leading order in μ 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.

The Regge limit of AdS3 holographic correlators with heavy states: towards the black hole regime

“…the CFT, we extend the results of [2,18] to arbitrarily high orders and elucidate the connection between bulk and CFT data.…”

“…The exact comparison between the bulk and boundary is currently beyond our reach for the microstate geometries that we are interested in due to the fact that the relevant 4point correlators are known only in terms of series. Since an analytic continuation is needed to go to the Regge regime of a correlator, we have to work perturbatively by expanding in the parameter [1,2,18]…”

“…For the relatively simple, though still quite non-trivial microstate geometry referred to as the (1,0,0) superstrata, some HHLL correlators can be evaluated exactly in µ in terms of a double Fourier series [29]. As is explored in greater detail in an upcoming publication [32], expanding this result in µ we obtain at each order a closed form expression in terms of generalised Bloch-Wigner functions [33] which here we use to extend the linear analysis of [2] to higher orders. For comparison, we review the analogous calculation for the case of the AdS spacetime with a conical defect of order k in three bulk dimensions [1,18].…”

“…In [2], this Regge limit analysis was applied to correlators involving pure heavy operators dual to smooth horizonless geometries with the same conserved charges and asymptotic behaviour as the Strominger-Vafa D1-D5-P black hole [24]. In the framework of the fuzzball proposal [25,26], such geometries -dual to pure states of the CFT -are considered to be at least a subset of the aforementioned black hole's microstates.…”

“…In the framework of the fuzzball proposal [25,26], such geometries -dual to pure states of the CFT -are considered to be at least a subset of the aforementioned black hole's microstates. Due to the lack of a closed form for the exact expressions of holographic 4-point correlation functions involving these heavy operators, the analysis of [2] was limited to first order in a perturbative expansion in the ratio between the reduced conformal weight of the heavy state h…”