Supersymmetry Ward identity for the supersymmetric non-Abelian gauge theory

Abstract

It is shown by direct computation that the supersymmetry Ward identity for the supersymmetric Yang-Mills theory can be satisfied at the one-loop level in the Wess-Zumino gauge when one uses dimensional regularization with the prescription ${\gamma }^{\mu }{\gamma }_{\mu }=4\mathrm{}$, and performs the Dirac algebra in four dimensions. The result is found to be valid for arbitrary covariant gauge-fixing functionals. A particular gauge, $\xi =-3\mathrm{}$, is found for which the supersymmetry transformations of both renormalized and unrenormalized fields are finite and well defined. In this same gauge, one-loop renormalization constants for two-, three-, and four-point one-particle-irreducible Green's functions are found to be equal.