N = 2 Morse-Liouville theory and non-minimal superconformal theories

We define and study the Morse-Liouville theory, i.e. a massive deformation of the N = 2, d = 2 Liouville model. Standard arguments of N = 2, d = 2 supersymmetry allow the computation of correlation functions and functions and fusion rules for subsets of (anti)chiral fields in the scaling regime, where N = 2 superconformal invariance is expected to be recovered. We find the relation c = 3(1+1/β²) > 3 between the coupling constant β and the central charge c of the scaling limit theory which is conjectured to represent sectors of non-minimal superconformal theories.