Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling

TL;DR

This paper computes exact large-N and strong coupling expressions for integrated correlators involving coincident Wilson lines and moment map operators in certain supersymmetric gauge theories, advancing understanding of non-perturbative dynamics.

Contribution

It introduces a novel class of integrated correlators involving coincident Wilson lines and derives their exact large-N and strong coupling results using supersymmetric localization.

Findings

Exact large-N expressions for correlators obtained.

Strong coupling expansions derived.

Results applicable to $ ext{SU}(N)$ gauge theories with supersymmetry.

Abstract

We consider two four-dimensional gauge theories with gauge group $SU(N)$: the $\mathcal{N}=4$ Super Yang-Mills (SYM) theory and the $\mathcal{N}=2$ quiver gauge theory obtained as a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM. In this context, we study a novel class of integrated correlators, namely those involving $n$-coincident Wilson lines and two moment map operators of conformal dimension two. By exploiting supersymmetric localization, we obtain exact expressions for these observables valid in the large-$N$ limit. Furthermore, using a combination of analytical and numerical methods, we derive their strong coupling expansions.