Four-point correlators in N=4 SYM from AdS$_5$ bubbling geometries

TL;DR

This paper computes an infinite family of four-point correlators in N=4 super Yang-Mills theory using supergravity backgrounds, confirming their consistency with superconformal Ward identities.

Contribution

It introduces a method to calculate four-point functions from non-trivial supergravity backgrounds related to LLM geometries, extending previous results to a broader class of correlators.

Findings

Derived all-light four-point correlators from supergravity backgrounds.

Confirmed superconformal Ward identities for these correlators.

Validated the supergravity approach for computing holographic correlators.

Abstract

Four-point correlation functions are observables of significant interest in holographic field theories. We compute an infinite family of four-point correlation functions of operators in short multiplets of 4D N=4 super Yang-Mills theory in the supergravity regime, by studying the quadratic fluctuations around non-trivial supergravity backgrounds. The supergravity backgrounds are supersymmetric smooth geometries in the family derived by Lin, Lunin and Maldacena. The light probes comprise an infinite sequence of Kaluza-Klein harmonics of the dilaton/axion. For generic parameter values, the supergravity backgrounds are dual to heavy CFT states. However we focus on the limit in which the dual CFT states become light single-particle states. The resulting all-light four-point correlators are related by superconformal Ward identities to previously known four-point correlators of half-BPS chiral primary operators. By verifying that the Ward identities are satisfied, we confirm the validity of the supergravity method.