Recent results on renormalization-group evolution of theories with gauge, fermion, and scalar fields

We discuss recent results on renormalization-group evolution of several types of theories. First, we consider asymptotically free vectorial gauge theories with various fermion contents and discuss higher-loop calculations of the UV to IR evolution in these theories, including an IR zero of the beta function and the value of the anomalous dimension γm at this point, together with comparisons with lattice measurements. Effects of scheme transformations are discussed. We then present a novel way to determine the value of NTC in an SU(NTC) technicolor model from a particular embedding in an extended technicolor theory. Finally, we analyze the renormalization-group behavior of several non-asymptotically free theories, including a U(1) gauge theory, a non-Abelian gauge theory with many fermions, an O(N) |4 scalar theory, and Yukawa theories.