Complete solution of 2D superfield supergravity from graded Poisson-sigma models, and the super point particle

Abstract

Recently an alternative description of 2D supergravities in terms of graded Poisson-sigma models (GPSM) has been given. As pointed out previously by the present authors a certain subset of GPSMs can be interpreted as ``genuine'' supergravity, satisfying the well-known limits of supergravity, albeit deformed by the dilaton field. In our present paper we show that precisely that class of GPSMs corresponds one-to-one to the known dilaton supergravity superfield theories presented a long time ago by Park and Strominger. Therefore, the unique advantages of the GPSM approach can be exploited for the latter: We are able to provide the first complete classical solution for any such theory. On the other hand, the straightforward superfield formulation of the point particle in a supergravity background can be translated back into the GPSM frame, where ``supergeodesics'' can be discussed in terms of a minimal set of supergravity field degrees of freedom. Further possible applications such as the (almost) trivial quantization are mentioned.