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

TL;DR

The paper constructs a novel closed-form perturbative two-mode LLM geometry in $AdS_5 imes S^5$ and analyzes its quadratic backreaction. By probing this background with a minimally coupled massless scalar, the authors derive two infinite sequences of holographic four-point correlators, which in the all-light limit relate to correlators of four single-particle CPOs via superconformal Ward identities. The correlators are presented in both position space (via $D$-functions) and Mellin space, with explicit checks against the Mellin-space bootstrap and Witten-diagram results; a new compact expression for one sequence of CPO correlators is obtained. The work demonstrates the viability of multi-mode LLM backgrounds for testing holographic duality and lays groundwork for further multi-mode and higher-order explorations in AdS/CFT. Overall, it strengthens the connection between backreacted smooth geometries and all-light CPO dynamics in ${ m N}=4$ SYM at strong coupling.

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 novel compact expression for one of the two infinite sequences of correlators of chiral primaries.