Relation between different auxiliary field formulations of N = 1 supergravity coupled to matter

We establish the connection between the old minimal set of auxiliary fields, the new minimal set and the Breitenlohner set. We show that the class of interactions which can be described by the latter two sets are particular cases of the interactions described in the old minimal set. The old and new minimal sets of auxiliary fields are equivalent for R-symmetric lagrangians. The precise correspondence of the bosonic part of the lagrangians in the two minimal formulations is exhibited. In particular, this equivalence shows that one can have both a Fayet-Iliopoulos term and spontaneously broken supersymmetry with vanishing cosmological constant.