/ 9505177 May . 1995 Four - Dimensional N = 2 ( 4 ) Superstring Backgrounds and The Real Heavens

We study N=2(4) superstring backgrounds which are four-dimensional nonKählerian with non-trivial dilaton and torsion fields. In particular we consider the case that the backgrounds possess at least one U(1) isometry and are characterized by the continual Toda equation and the Laplace equation. We obtain a string background associated with a non-trivial solution of the continual Toda equation, which is mapped, under the T-duality transformation, to the hyperKähler Taub-NUT instanton background. It is shown that the integrable property of the non-Kählerian spaces have the direct origin in the real heavens: real, selfdual, euclidean, Einstein spaces. The Laplace equation and the continual Toda equation imposed on quasi-Kähler geometry for consistent string propagation are related to the self-duality conditions of the real heavens with “translational” and “rotational” Killing symmetry respectively. ⋆ e-mail: [email protected]