Generalized Supergravity in Two Dimensions

TL;DR

This paper extends two-dimensional supergravity by relaxing torsion constraints, simplifying calculations with inverse supervierbein, and exploring non-Einsteinian models relevant for super black holes and string theory.

Contribution

It introduces a new method using inverse supervierbein to solve supergravity constraints and clarifies the relation between functions and supergravity multiplets, enabling novel model constructions.

Findings

Simplified supergravity constraint solutions using inverse supervierbein.

Clarified the relation between functions in Howe's work and supergravity multiplets.

Presented explicit models with nontrivial curvature and torsion, some with dilatonic formulations.

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 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, how to construct `non-Einsteinian' supergravity theories with nontrivial 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 a dilatonic formulation for the bosonic part of the action.