A note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory

TL;DR

This paper introduces a simplified method to analyze the saddle point equation for Wilson loops in N=2 super Yang-Mills theory at strong coupling, providing explicit eigenvalue density and free energy expressions.

Contribution

It presents an alternative approximation technique for the integral equation, enabling exact solutions and explicit formulas, with comparison to existing methods for validation.

Findings

Derived explicit eigenvalue density expression.

Calculated planar free energy using the approximation.

Compared results with previous studies for accuracy.

Abstract

We propose an alternative method to study the saddle point equation in the strong coupling limit for the Wilson loop in $\mathcal{N}=2$ D=4 super Yang-Mills with an SU(N) gauge group and 2N hypermultiplets. This method is based on an approximation of the integral equation kernel which allows to solve the simplified problem exactly. To determine the accuracy of this approximation, we compare our results to those obtained recently by Passerini and Zarembo. Although less precise, this simpler approach provides an explicit expression for the density of eigenvalues that is used to derive the planar free energy.