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

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 γ⁵ 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 $\text{?·J}{}^5\text{～ β(g)F}\text{F}\text{?}$ are discussed.