$1/N$ expansion of circular Wilson loop in $\mathcal N=2$ superconformal $SU(N)\times SU(N)$ quiver

TL;DR

This paper investigates the $1/N^2$ correction to the circular Wilson loop in a specific $ ext{N}=2$ superconformal quiver gauge theory, using localization, string theory insights, and numerical analysis to understand its behavior at weak and strong coupling.

Contribution

It provides the first detailed analysis of the $1/N^2$ correction in the Wilson loop for the $ ext{N}=2$ orbifold theory, connecting gauge theory calculations with string theory predictions.

Findings

The $1/N^2$ term has the same strong-coupling asymptotics as in $ ext{N}=4$ SYM.

Numerical support for the predicted behavior of the Wilson loop correction.

A relation between the $1/N^2$ correction and the derivative of the free energy on the 4-sphere.

Abstract

Localization approach to $\mathcal N=2$ superconformal $SU(N) \times SU(N)$ quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular $SU(N)$ Wilson loop $\langle\mathcal W\rangle$. We study the subleading $1/N^2$ term in the large $N$ expansion of $\langle\mathcal W\rangle$ at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the $\mathbb Z_{2}$ orbifold of the $SU(2N)$ $\mathcal N=4$ SYM theory. This orbifold gauge theory should be dual to type IIB superstring in ${\rm AdS}_5\times (S^{5}/\mathbb Z_{2})$. We present a string theory argument suggesting that the $1/N^2$ term in $\langle\mathcal W\rangle$ in the orbifold theory should have the same strong-coupling asymptotics $ \lambda^{3/2}$ as in the $\mathcal N=4$ SYM case. We support this prediction by a numerical study of the localization matrix model on the gauge theory side. We also find a relation between the $1/N^2$ term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.