Graded Poisson-Sigma Models and Dilaton-Deformed 2D Supergravity Algebra

TL;DR

This paper establishes a clear connection between graded Poisson-Sigma models and supergravity algebras, resolving ambiguities and obstructions in fermionic extensions of 2D gravity theories, and identifying conditions for unique, singularity-free models.

Contribution

It relates gPSM algebra constraints to supergravity algebras, showing that under natural assumptions, ambiguities and obstructions are eliminated, leading to unique fermionic extensions.

Findings

Unique fermionic extensions for key 2D gravity models

Elimination of ambiguities and obstructions in supergravity extensions

Identification of superspace supergravity as a special case

Abstract

Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algebras which can be interpreted as supergravities in the usual sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them --like demanding rigid supersymmetry in a certain flat limit, or linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint-- in the ``genuine'' supergravity obtained in this way the ambiguities disappear, as well as the obstructions referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.)\ under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.