Universality of giant graviton correlators

TL;DR

This work computes exact planar HHLL integrated correlators in $\mathcal{N}=4$ SYM with two light half-BPS insertions and two heavy giant-graviton insertions, realized either as sphere or AdS D3-branes. Using supersymmetric localisation and a matrix-model framework, the authors obtain all-$\lambda$ expressions for the integrated correlators and show that their strong-coupling asymptotic expansions coincide, signaling a universal structure for D-brane scattering amplitudes. Despite identical leading strong-coupling behavior, differences among the correlators arise in non-perturbative, exponentially suppressed sectors, which are analyzed via resurgence methods and holographic interpretations. The results extend to a related $USp(2N)$ theory with D7-branes, revealing a striking universality across distinct brane scattering processes and offering insights into Coulomb-branch physics and large-charge limits. The paper also discusses potential extensions to non-planar corrections, other integrated correlators, and the relation to modular (Eisenstein) completions of these observables.

Abstract

We study a class of heavy-heavy-light-light (HHLL) integrated correlators of superconformal primary operators in $SU(N)$ $\mathcal{N}=4$ super Yang-Mills theory involving two light operators from the stress-tensor multiplet and two heavy operators whose conformal dimensions are proportional to the number of colours $N$. In the large-$N$ limit these heavy operators are dual to sphere and AdS giant gravitons, realised holographically as D3-branes wrapping an $S^3$ inside either the $S^5$ or the $AdS_5$ factor of the $AdS_5 \times S^5$ background geometry. These HHLL correlators thus describe the scattering of two gravitons off D3-branes. In the planar limit we derive exact expressions for the HHLL integrated correlators as functions of both the 't Hooft coupling and the giant graviton dimension. Remarkably, despite exhibiting distinct perturbative expansions at weak coupling, these integrated correlators share the same universal asymptotic series at strong coupling. We also demonstrate that a seemingly unrelated integrated correlator in a $USp(2N)$ $\mathcal{N}=2$ gauge theory, holographically dual to gluon-graviton scattering off D7-branes, exhibits precisely the same strong coupling asymptotic series. This reveals a striking universality of D-brane scattering processes. Furthermore, we compute the exponentially suppressed corrections at strong coupling for all these observables, showing that they are precisely the non-perturbative effects that account for the differences between these integrated correlators beyond the universal asymptotic series. Finally, we comment on the resurgent properties and the holographic interpretation of these exponentially suppressed terms.