Holographic 4-point correlators with heavy states

TL;DR

This work develops a holographic framework to compute 4-point correlators with two heavy and two light operators in AdS3/CFT2 by analyzing quadratic fluctuations around heavy D1-D5 geometries. The authors perform a gravity calculation in a detailed perturbative expansion around AdS3×S3, obtaining a concrete HHLL correlator at strong coupling that is not protected compared to the orbifold point; the result is expressed in terms of AdS3 bulk-to-boundary propagators and D-integrals, with a leading disconnected piece and a nontrivial O(N0) correction encoding the heavy geometry interior. The analysis reveals logarithmic contributions and anomalous dimensions in the OPE, highlighting dynamical effects tied to the heavy state's microstate geometry. Overall, the paper provides a robust method to extract dynamical 4-point data at strong coupling in AdS3/CFT2 and clarifies how heavy-state backgrounds alter correlators relative to free CFT predictions.

Abstract

The AdS/CFT duality maps supersymmetric heavy operators with conformal dimension of the order of the central charge to asymptotically AdS supergravity solutions. We show that by studying the quadratic fluctuations around such backgrounds it is possible to derive the 4-point correlators of two light and two heavy states in the supergravity approximation. We provide an explicit example in the AdS$_3$ setup relevant for the duality with the D1-D5 CFT. Contrary to previously studied examples, the supergravity correlator derived in this work differs from the result obtained at the CFT orbifold point. Our method bypasses the difficulties of applying the standard Witten's diagrams approach to correlators with operators of large conformal dimension and also avoids some technical steps that have made the computation of dynamical 4-point correlators in the AdS$_3$/CFT$_2$ context unfeasible until now.