Higher rank Wilson loops in the $\mathcal{N} = 2$ $SU(N)\times SU(N)$ conformal quiver

TL;DR

This paper calculates the expectation values of higher rank Wilson loops in specific representations within an $ ext{SU}(N) imes ext{SU}(N)$ $ ext{N}=2$ SCFT using a matrix model, exploring their relation to $ ext{N}=4$ SYM.

Contribution

It provides explicit computations of Wilson loops in higher rank representations for the $ ext{A}_1$ quiver $ ext{N}=2$ SCFT and examines their connection to a universal coupling renormalization conjecture.

Findings

Wilson loop expectation values computed for symmetric and antisymmetric representations.

Results support the conjecture relating $ ext{N}=2$ SCFT observables to $ ext{N}=4$ SYM via coupling renormalization.

The matrix model approach effectively captures the behavior of these observables.

Abstract

In this note we compute the expectation value of a circular BPS Wilson loop in the higher rank totally symmetric and antisymmetric representations of SU(N) in the $\hat{A}_1$ quiver $\mathcal{N} = 2$ SCFT, using a matrix model. We discuss the connection with a recent conjecture stating that expectation values of observables in this sector are obtained from $\mathcal{N = 4}$ SYM by a universal renormalization of the `t Hooft coupling.