Universality of giant graviton correlators

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.