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.
Highlights
Be approximated by a null geodesic that begins and ends on the asymptotic AdS boundary of the geometry
We examine the Regge limit of holographic 4-point correlation functions in AdS3 × S3 involving two heavy and two light operators
As the probe traverses the spacetime it accumulates a phase; the details of which contains rich information about the interaction between the probe and the heavy object. This phase shift can be used to analyse the Regge limit of a CFT 4-point function containing two heavy and two light operators (HHLL), as demonstrated in [1]. This setup was used to extract the eikonal phase for AdS black holes and conical defects, which in the case of two-dimensional CFTs was matched to the behaviour of the HHLL Virasoro vacuum block [11, 12] in the Regge limit, emphasising the dominance of the stress tensor sector in this kinematical regime
Summary
The physical process of interest here is the scattering of a highly energetic light particle from a heavy object in asymptotically AdS3 spacetimes. One can study such an experiment by approximating the path of the probe with a null geodesic in the spacetime obtained from the backreaction of the heavy object. This scattering can be equivalently described in the dual two-dimensional CFT: there one needs to analyse the Regge limit of a 4-point correlation function with two heavy and two light operators, dual to the classical spacetime and light probe respectively. We present the gravitational and field-theoretic set-up necessary to describe such a scattering process and present the proposal of [1], which relates the phase shift acquired by a null geodesic as it traverses an asymptotically AdS spacetime to the Regge limit of a 4-point correlation function in the dual CFT. The CFT, we extend the results of [2, 18] to arbitrarily high orders and elucidate the connection between bulk and CFT data
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