The supercurrent and the Adler-Bardeen theorem

When supersymmetric theories are regularized by dimensional reduction in superspace the supercurrent is a n-vector and the breaking of superconformal invariance by the regularization gives rise to supertrace anomalies proportional to the β-function. We construct the composite renormalized operator that describes it and study its properties. We construct a distinct four-dimensional composite operator and show that its first component satisfies the Adler-Bardeen theorem. Our results are based on explicit calculations through two-loop order for both the Wess-Zumino model and SSYM, using the background field method and covariant supergraphs. (orig.)