On N=4 extended super-Liouville theory

We examine the coupling of two-dimensional, N=4 extended supergravity to N = 4 supersymmetric matter systems. In the superconformal gauge, the effective action for the gravity supermultiplet, i.e. the N=4 super-Liouville action is derived. We also determine the supergravitational dressing of matter primary fields transforming in the so-called "massless" representations of the N=4 superalgebra, and the corresponding scaling properties of the partition function. Finally some applications to non-critical string-like models propagating in quaternionic spaces are discussed.