Geometrical constraints on supergravity coupling

The description of supergravity requires the imposition of constraints the various choices of which correspond to various possible sets of axuiliary fields which can influence the possibilities of coupling to matter fields. This paper shows that the minimal, as opposed to the non-minimal or the new-minimal, set of auxiliary fields is the most versatile in that although they imply conformally invariant couplings in the kinetic terms of the scalar multiplet matter fields, they permit arbitrary scalar multiplet self-interactions. Linearized supergravity, matter coupling, self-interactions of matter fields, and the vanishing volume of superspace and the action for new-minimal supergravity are reviewed