Holographic correlators from multi-mode AdS$_5$ bubbling geometries

TL;DR

This paper constructs a new supergravity solution involving linearized gravitons and their backreaction to compute four-point correlators in the dual 4D super Yang-Mills theory, confirming previous results and providing new explicit formulas.

Contribution

It introduces a novel perturbative LLM supergravity solution with mixed mode gravitons, enabling computation of new four-point correlators in the dual field theory.

Findings

Computed two infinite sequences of four-point correlators.

Confirmed existing expressions for correlators of chiral primary operators.

Provided a new explicit formula for one sequence of correlators.

Abstract

Supergravity calculations of holographic four-point correlation functions are a powerful tool for deriving dynamical information about the dual field theory at strong coupling. Recently, a number of such computations have been performed by studying light probes of smooth horizonless supergravity solutions, including certain asymptotically AdS$_5 \times$S$^5$ solutions of Lin-Lunin-Maldacena (LLM) type. We construct a new closed-form perturbative LLM solution involving a pair of linearized supergravitons with different mode numbers and their quadratic backreaction. Using this solution, we compute two infinite sequences of four-point correlators. Depending on the scaling of certain parameters, the background supergravity solutions are dual to states of 4D $\mathcal{N}=4$ super Yang-Mills theory that are either heavy or light, whereupon the correlators in the dual field theory are either (perturbatively) heavy-heavy-light-light or all-light. In the all-light regime, the correlators we compute are related by superconformal Ward identities to correlators of four single-particle chiral primary operators (CPOs). We confirm a set of expressions in the literature for such correlators of CPOs, that were obtained via Mellin space bootstrap and/or Witten diagram methods. We also obtain a new explicit compact expression for one of the two infinite sequences of correlators of chiral primaries. The method we present is capable of accessing correlators with an arbitrary degree of extremality.