Universality classes of matrix models in 4-έ dimensions

The role that matrix models, in (4-έ) dimensions, play in quantum critical phenomena is explored. We begin with a traceless Hermitean scalar matrix model and add operators that couple to fermions, and gauge fields. Through each stage of generalization the universality class of the resulting theory is explored. We also argue that chiral symmetry breaking in (2 + 1) dimensional Q C D can be identified with Neel ordering in two dimensional quantum antiferromagents. When operators that drive the phase transition are added to these theories, we postulate that the resulting quantum critical behavior lies in the universality class of gauged Yukawa matrix models. As a consequence of the phase structure of this matrix model, the chiral transition is typically of first order with computable critical exponents.Science, Faculty ofPhysics and Astronomy, Department ofGraduat