Super-Liouville action for Regge surfaces

We compute the super-Liouville action for a two-dimensional Regge surface b y exploiting the invariance of the theory under the superconformal group fo r sphere topology and under the supermodular group for torus topology. For sphere topology and torus topology with even spin structures, the action is completely fixed up to a term which in the continuum limit goes over to a topological invariant, while the overall normalization of the action can be taken from perturbation theory. For the odd spin structure on the torus, d ue to the presence of the fermionic supermodulus, the action is fixed up to a modular invariant quadratic polynomial in the fermionic zero-modes. (C) 1993 Published by Elsevier Science B.V.