Target-Superspace in 2d Dilatonic Supergravity

TL;DR

This paper reformulates 2d N=1 dilatonic supergravity as a graded Poisson Sigma Model, revealing invariance properties and providing general solutions, while establishing classical equivalence with the bosonic theory.

Contribution

It introduces a graded Poisson Sigma Model framework for 2d N=1 supergravity, enabling explicit solutions and demonstrating classical equivalence with the bosonic case.

Findings

General local solutions to field equations derived

Invariance under diffeomorphisms and superdiffeomorphisms established

Classical equivalence between supersymmetric and bosonic theories shown

Abstract

The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson Sigma Model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton, which is the generator of Lorentz boosts therein. The Poisson bracket on the target space induces the invariance of the worldsheet theory against both diffeomorphisms and local supersymmetry transformations (superdiffeomorphisms). The machinery of Poisson Sigma Models is then used to find the general local solution to the field equations. As a byproduct, classical equivalence between the bosonic theory and its supersymmetric extension is found.