Matrix models for extremal and integrated correlators of higher rank

TL;DR

This paper develops a dual matrix model framework combining Wishart and Jacobi models to analyze extremal and integrated correlators of half-BPS operators in 4D supersymmetric gauge theories at large R-charge, capturing weak and strong coupling behaviors.

Contribution

It introduces a novel coupled Wishart-Jacobi matrix model approach for large R-charge correlators in 4D $ ext{SU}(3)$ gauge theories, with potential extension to higher N.

Findings

Matrix models describe correlators at large R-charge.

Behavior at weak and strong coupling is extracted.

Nonperturbative corrections are included.

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.