Wilson loops in antisymmetric representations from localization in supersymmetric gauge theories

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.