Graded Poisson - Sigma Models I : Complete Actions and Their Symmetries

The formalism of graded Poisson-Sigma models allows the construction of N = (2, 2) dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions , is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of superfields is presented, although for the latter so far only the bosonic part of the action seems to have been available in the literature. It is shown how un-gauged models can be obtained in a systematic way and some relations to relevant literature in superstring theory are discussed.