The Complete Solution of 2D Superfield Supergravity from graded Poisson-Sigma Models and the Super Pointparticle

TL;DR

This paper establishes a one-to-one correspondence between certain graded Poisson-Sigma models and known dilaton supergravity theories, providing the first complete classical solutions and insights into supergeodesics and potential quantization.

Contribution

It demonstrates that a specific class of gPSMs exactly matches known supergravity theories, enabling complete classical solutions and new perspectives on supergeodesics and quantization.

Findings

Complete classical solutions for supergravity theories derived from gPSMs.

Identification of a one-to-one correspondence between gPSMs and supergravity superfield theories.

Discussion of supergeodesics and potential for simplified quantization.

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, fulfilling 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 like the (almost) trivial quantization are mentioned.