Generalized supergravity in two dimensions

Abstract

Among the usual constraints of (1,1) supergravity in d = 2 the condition of vanishing bosonic torsion is dropped. Using the inverse supervierbein and the superconnection considerably simplifies the formidable computational problems. It allows us to solve the constraints for those fields before taking into account the (identically fulfilled) Bianchi identities. The relation of arbitrary functions in the seminal paper of Howe to supergravity multiplets is clarified. The local supersymmetry transformations remain the same, but, somewhat surprisingly, the transformations of zweibein and Rarita-Schwinger field decouple from those of the superconnection multiplet. A method emerges naturally of how to construct ‘non-Einsteinian’ supergravity theories with non-trivial curvature and torsion in d = 2 which, apart from their intrinsic interest, may be relevant for models of super black holes and for novel generalizations in superstring theories. Several explicit examples of such models are presented, some of which immediately allow for a dilatonic formulation for the bosonic part of the action.