CONFORMAL-TRANSFORMATION PROPERTIES OF THE SUPERCURRENT IN 4-DIMENSIONAL SUPERSYMMETRIC THEORIES

We investigate the superconformal transformation properties of Green f unctions with one or more insertions of the supercurrent in N =1 super symmetric quantum field theories. These Green functions are convenient ly obtained by coupling the supercurrent and its trace to a classical supergravity background. We derive fiat space superconformal Ward iden tities from diffeomorphisms and Weyl transformations on curved supersp ace. For the classification of potential quantum superconformal anomal ies in the massless Wess-Zumino model on curved superspace a perturbat ive approach is pursued, using the BPHZ scheme for renormalisation. By deriving a local Callan-Symazik equation the usual dilatational anoma lies are identified and it is shown that no further superconformal ano malies involving the dynamical fields are present. (C) 1998 Elsevier S cience B.V.