Matrix models for extremal and integrated correlators of higher rank

Abstract

We study extremal and integrated correlators of half-BPS operators in four-dimensional $\mathcal{N}=2$ SQCD and $\mathcal{N}=4$ SYM with $SU(3)$ gauge group. We focus on the large R-charge sector where the number of operators insertions becomes very large. In this regime, we demonstrate that the correlators are described by a combination of Wishart and Jacobi matrix models, coupled in a non-trivial way. The size of the matrices in each model corresponds to the maximal number of insertions for each of the two single trace generators. This dual matrix model representation allows us to extract the behavior of the correlators at weak and strong coupling in a 't Hooft-like double scaling limit, including nonperturbative corrections. Although this work focuses on $SU(3)$, we expect that our techniques can be extended to $SU(N)$ for $N>3$ as well.