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

TL;DR

This work develops a non-perturbative, modularly invariant framework for integrated four-point correlators in ${ m N}=4$ SYM, focusing on maximal-trace and coherent-state insertions. By combining ${ m SL}(2,Z)$ spectral theory, localization, and modular resurgence, the authors derive exact transseries expansions in large-$N$ and large-charge regimes, linking the field theory results to holographic back-reactions in AdS$_5 imes$S$^5$ via AdS bubbles and LL-M geometries. They uncover a rich structure of non-perturbative corrections, including Cheshire-cat resurgence for finite $N$, and three distinct non-perturbative scales in the heavy regime, which they corroborate with giant-magnon spectra on the AdS bubble. A central result is the exact genus-zero mapping between HHLL and maximal-trace correlators under a parameter redefinition, along with a precise holographic interpretation in terms of Virasoro–Shapiro amplitudes on the AdS bubble. Overall, the paper provides a robust non-perturbative bridge between exact integrated correlators in ${ m N}=4$ SYM and the geometry and dynamics of bubbling AdS spacetimes, offering quantitative predictions for stringy and quantum gravity corrections in holography.

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 $τ$. 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.