BPS Wilson loop in $\mathcal N=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation

TL;DR

This paper studies the expectation value of a BPS Wilson loop in a specific ${ m extbf{N}=2}$ superconformal $SU(N)$ gauge theory, confirming a universal $ ext{lambda}^{3/2}$ scaling of non-planar corrections at strong coupling through analytic and numerical methods.

Contribution

It predicts and confirms the universal $ ext{lambda}^{3/2}$ scaling of the leading non-planar correction in the Wilson loop expectation value for a class of ${ m extbf{N}=2}$ theories, extending previous results.

Findings

Confirmed the $ ext{lambda}^{3/2}$ scaling of non-planar corrections.

Validated predictions using both analytic localization and numerical resummation.

Showed the model's duality to an orbifold/orientifold of AdS$_5\times S^5$.

Abstract

We consider the expectation value $\langle \cal W \rangle$ of the circular BPS Wilson loop in ${\cal N}=2$ superconformal $SU(N)$ gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This model admits a regular large $N$ expansion, is planar-equivalent to ${\cal N}=4$ SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS$_5\times S^5$ superstring theory. On the string theory side $\langle\cal W \rangle $ is represented by the path integral expanded near the same AdS$_2$ minimal surface as in the maximally supersymmetric case. Following the string theory argument in arXiv:2007.08512, we suggest that as in the ${\cal N}=4$ SYM case and in the ${\cal N}=2$ $SU(N) \times SU(N)$ superconformal quiver theory discussed in arXiv:2102.07696, the coefficient of the leading non-planar $1/N^2$ correction in $\langle\cal W \rangle $ should have the universal $\lambda^{3/2}$ scaling at large 't Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for $\langle\cal W \rangle $. We complement the analytic derivation of the $\lambda^{3/2}$ scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Pad\'e analysis.