Gauged Yukawa Matrix Models and 2-Dimensional Lattice Theories

Abstract

We argue that chiral symmetry breaking in three dimensional QCD can be identified with N\'eel order in 2-dimensional quantum antiferromagnets. When operators which drive the chiral transition are added to these theories, we postulate that the resulting quantum critical behavior is in the universality class of gauged Yukawa matrix models. As a consequence, the chiral transition is typically of first order, although for a limited class of parameters it can be second order with computable critical exponents.