Quantization of 2D dilaton supergravity with matter

General N=(1,1) dilaton supergravity in two dimensions allows a backgroundindependent exact quantization of the geometric part, if these theories areformulated as specific graded Poisson-sigma models. The strategy developed forthe bosonic case can be carried over, although considerable computationalcomplications arise when the Hamiltonian constraints are evaluated in thepresence of matter. Nevertheless, the constraint structure is the same as inthe bosonic theory. In the matterless case gauge independent nonlocalcorrelators are calculated non-perturbatively. They respect local quantumtriviality and allow a topological interpretation. In the presence of matterthe ensuing nonlocal effective theory is expanded in matter loops. The lowestorder tree vertices are derived and discussed, entailing the phenomenon ofvirtual black holes which essentially determine the corresponding S-matrix. Notall vertices are conformally invariant, but the S-matrix is invariant, asexpected. Finally, the proper measure for the 1-loop corrections is addressed.It is argued how to exploit the results from fixed background quantization forour purposes.Comment: 40p LaTeX, JHEP style, 3 eps figures. v2: typo