Four-dimensional gravitational backgrounds based on [formula omitted], superconformal systems

Abstract

We propose two new realizations of the N = 4, c ̂ = 4 superconformal system based on the compact and non- compact versions of parafermionic algebras. The target space interpretation of these systems is given in terms of four- dimensional target spaces with non-trivial metric and topology different from the previously known four-dimensional semi-wormhole realization. The proposed c ̂ = 4 systems can be used as a building block to construct perturbatively stable superstring solutions with covariantized target space supersymmetry around non-trivial gravitational and dilation backgrounds.