Wilson Loops in Antisymmetric Representations from Localization in Supersymmetric Gauge Theories

Abstract

Large-[Formula: see text] phase transitions occurring in massive [Formula: see text] 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: [Formula: see text] SQCD with various mass arrangements and [Formula: see text] theory. As a byproduct, we solve planar [Formula: see text] SQCD with three independent mass parameters. This model has two effective mass scales and undergoes two phase transitions. In memory of Ludvig Dmitrievich Faddeev