Dynamics of Heavy Operators in $\mathcal{N}=4$ SYM: Integrated Correlators and AdS Bubbles

TL;DR

This paper explores the behavior of integrated correlators in $ ext{SU}(N)$ $ ext{N}=4$ SYM, revealing non-perturbative effects and holographic duals involving AdS bubbles, through advanced spectral and resurgence techniques.

Contribution

It introduces a novel analysis of large-$N$ and large-charge expansions, deriving exact correlators and connecting them to AdS bubble geometries in holography.

Findings

Exact expression for a new integrated correlator involving coherent-state operators.

Identification of non-perturbative effects linked to giant-magnon configurations.

Agreement between supergravity calculations and explicit correlator integrations.

Abstract

We study integrated correlation functions of half-BPS operators in $SU(N)$ $\mathcal{N} = 4$ supersymmetric Yang-Mills theory (SYM) involving two superconformal primary operators in the stress-tensor multiplet and two identical maximal-trace operators of arbitrary $R$-charge $p$. Thanks to $\mathcal{N}=4$ SYM electro-magnetic duality these integrated correlators have recently been computed as exact functions of $N$, $p$, and of the Yang-Mills complexified coupling $\tau$. Using a combination of tools from ${\rm SL}(2,\mathbb{Z})$ spectral theory and resurgence analysis, we study the landscape of large-$N$ and/or large-charge expansions for these correlators. In particular, we find novel non-perturbative effects in the limit where $N\rightarrow \infty$ with $p/N^2$ fixed. From a holographic point of view this double-scaling regime is deeply connected with a second family of correlators which we analyse. Using the results for the maximal-trace operators, we derive an exact expression for a new integrated correlator involving two coherent-state operators, defined via an exponential generating function of multi-graviton states. At large-$N$ this correlator admits a holographic dual description in terms of a back-reacted geometry known as the AdS bubble. First, we show that the leading supergravity contribution to the integrated correlator agrees with a direct explicit integration of the correlator itself. Secondly, we derive predictions for the integrated version of the Virasoro-Shapiro amplitude evaluated on the AdS bubble background. Lastly, we demonstrate that the large-$N$ non-perturbative contributions to this integrated correlator emerge from giant-magnon configurations in the dual AdS bubble.