2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192164We propose two new realizations of the N=4, $\hat{c}=4$ 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 $\hat{c}=4$ systems can be used as a building block to construct perturbatively stable superstring solutions with covariantized target space supersymmetry around non-trivial gravitational and dilaton backgrounds.LateX, 21ppHigh Energy Physics - Theorytext