Wilson loops in antisymmetric representations from localization in supersymmetric gauge theories

TL;DR

This paper studies phase transitions in large-N supersymmetric gauge theories by analyzing Wilson loops in antisymmetric representations, revealing second-order phase transitions linked to the free energy behavior.

Contribution

It introduces a novel approach to probe phase transitions in N=2 theories using Wilson loops and solves a complex N=2 SQCD model with multiple mass parameters.

Findings

Wilson loops exhibit second-order phase transitions.

Effective free energy describes Wilson loop behavior.

The N=2 SQCD with three masses undergoes two phase transitions.

Abstract

Large-N phase transitions occurring in massive N=2 theories can be probed by Wilson loops in large antisymmetric representations. The logarithm of the Wilson loop is effectively described by the free energy of a Fermi distribution and exhibits second-order phase transitions (discontinuities in the second derivatives) as the size of representation varies. We illustrate the general features of antisymmetric Wilson loops on a number of examples where the phase transitions are known to occur: N=2 SQCD with various mass arrangements and N=2* theory. As a byproduct we solve planar N=2 SQCD with three independent mass parameters. This model has two effective mass scales and undergoes two phase transitions.