Self-Dual Supergravity from N = 2 Strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma model is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in {alpha}{prime}, all in superspace. The resulting field equations describe N = 1 self-dual supergravity