Dimensional regularization and the two-loop axial anomaly in abelian, non-abelian and supersymmetric gauge theories

Abstract

The two-loop corrections to the axial anomaly are calculated for a non-abelian gauge theory with fermions using both conventional and supersymmetric dimensional regularization. In both cases we find results consistent with the Adler-Bardeen theorem if we use non-anticommuting [gamma]5 of 't Hooft and Veltman. Expectations (based on the supermultiplet structure of the anomalies) that there exists in N = 1 supersymmetric Yang-Mills theory an axial current J5 such that are discussed.