On the Ultraviolet to Infrared Evolution of Chiral Gauge Theories

We discuss the ultraviolet (UV) to infrared (IR) evolution of asymptotically free chiral gauge theories. Various types of IR behavior are considered, including confinement without spontaneous chiral symmetry breaking, and formation of bilinear fermion condensates that preserve or dynamically break the chiral gauge invariance. We compare different schemes for the study of this evolution and the resultant IR structure of the theories, including a conjectured inequality based on the counting of degrees of freedom. We note some new patterns of UV to IR evolution.