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

Abstract

We examine the Regge limit of holographic 4-point correlation functions in AdS3× S3 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 CFT2’s central charge, thus going beyond the low order results of [1] and [2]. 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 AdS3 conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.

Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena

“…• Our computation is also similar to holographic computations of four-point correlators with two heavy and two light operators, where the two heavy operators make black holes or conical defect geometries in the bulk picture (see, for example, [34,[51][52][53][54][55][56][57][58]). Virasoro blocks or multi-trace exchange diagrams in the eikonal approximation can be expressed as the sum of global conformal blocks, which correspond to crossed-ladder diagrams.…”

Supercharged AdS3 Holography

“…This enabled new results on LLLL four-point functions to be derived [83][84][85][86][87]. More recently, HHLL correlators in the Regge limit have been computed [88,89], including those in which the light operators are multi-trace operators [90]. Our results on resolving the operator mixing among light operators should enable new classes of four-point functions to be studied.…”

Real-Time Holography and Hybrid WKB for BTZ Wormholes

“…In our convention the minus appearing in front of the action on γ 2 cancels with the minus coming from the fact that the derivation −∂ τ on γ b runs in the opposite direction compared to the derivation i∂ t on γ 2 , thus (B.6) applies universally at all meeting hypersurfaces. 22 A Euclidean mode will satisfy exactly the same radial equation as a Lorentzian one, since e.g. e iωt g L,tt ∂ 2 t e −iωt = e ωτ g E,τ τ ∂ 2 τ e −ωτ (similar relations hold involving off-diagonal time-space components of the metric).…”

“…The radial parts f i , f I then obey the same second-order ODE, 22 which needs to be supplied with two boundary conditions. If the geometry in question has only one boundary (e.g.…”

“…1 One can probe these microstate geometries with a light field (that does not backreact) such as a scalar; a quantity of interest is thus the two-point function of such a light field in a particular supergravity background. This corresponds in the dual CFT to a four-point correlation function ∼ HLLH of two light operators L (for the light probe) and two heavy operators H (for the background state), and can, in some cases, be studied using CFT methods [20,21,22,23].…”