The consistent chiral anomaly in supersymmetric Yang-Mills theories

Abstract

By means of algebraic methods we find a solution of the consistency conditions obeyed by the chiral anomaly in SYM theories. The latter consists of a chiral gauge anomaly which breaks rigid supersymmetry and of a supersymmetric partner. We prove that the supersymmetric partner can be eliminated by adding a suitable counterterm to the action. The gauge anomaly obtained by varying the new action is shown to be supersymmetric invariant. We give an explicit expression of it. We also show the equivalence of the expression of consistent chiral anomalies in different formulations of SYM theories.