Target-superspace in 2d dilatonic supergravity

The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson σ-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 σ-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.