Conformal Transformation Properties of the Supercurrent in Four Dimensional Supersymmetric Theories

We investigate the superconformal transformation properties of Green functions with one or more insertions of the supercurrent in N=1 supersymmetric quantum field theories. These Green functions are conveniently obtained by coupling the supercurrent and its trace to a classical supergravity background. We derive flat space superconformal Ward identities from diffeomorphisms and Weyl transformations on curved superspace. For the classification of potential quantum superconformal anomalies in the massless Wess-Zumino model on curved superspace a perturbative approach is pursued, using the BPHZ scheme for renormalisation. By deriving a local Callan-Symanzik equation the usual dilatational anomalies are identified and it is shown that no further superconformal anomalies involving the dynamical fields are present.