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

TL;DR

The paper computes integrated correlators built from $n$ coincident Wilson lines and two moment-map operators in $SU(N)$ $\mathcal{N}=4$ SYM and a $\mathbb{Z}_2$ orbifold $\mathcal{N}=2$ quiver, using supersymmetric localization to map to mass-deformed matrix models and extracting exact large-$N$ results. It derives the leading three terms in the $1/N$ expansion and provides exact, parameter-dependent strong-coupling expansions, with the planar term scaling linearly with $n$ and explicit results for twisted, untwisted, and mixed Wilson-line configurations. The work verifies $n=1$ benchmarks against known results and extends to multi-line, multi-sector observables, offering nonperturbative data that informs holographic interpretations and constrains unintegrated defect correlators via Mellin amplitude techniques. These results advance understanding of nonperturbative dynamics in highly supersymmetric gauge theories and lay groundwork for exploring very strong coupling and multi-node quivers.

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.

Figures (2)

• Figure 1: The $4d$$\mathcal{N}=2$ two nodes quiver gauge theory.
• Figure 2: Ratio between $\mathcal{I}^{\text{even}}$ and $W_{\text{con}}^{(2)}$ as a function of the 't Hooft coupling. We observe that this function reaches a plateau for values of $\lambda \geq 10^4$. The blue line represents the value of the coefficient $c_0^{\text{even}}$ obtained by fitting the numerical data (black dots) with the ansatz \ref{['ansatz']}.