The two-loop axial anomaly in N = 1 supersymmetric Yang-Mills theory

Abstract

We calculate the two loop correction to the divergence of the axial current in N = 1 supersymmetric Yang-Mills theory. We find that, if we use supersymmetric dimensional regularization, the anomaly is proportional to the β-function, a result we interpret as evidence that the supermultiplet nature of the trace, axial and supersymmetry anomalies persists at the two- loop level. Thus it appears that the Adler-Bardeen theorem is not valid in supersymmetric theories.