Construction of the quantum supersymmetric Liouville theory for string models

Abstract

We construct the quantum supersymmetric Liouville theory with regard to applications to string models. We find the supersymmetric analogue of the triangle relation discovered by Gervais and Neveu in the purely bosonic case. Restricting ourselves to the weak coupling region, the resulting string theory is free of ghosts and tachyons in space-time dimension D⩽1.