Four-Dimensional N=2(4) Superstring Backgrounds and The Real Heavens

Details Four-Dimensional N=2(4) Superstring Backgrounds and The Real Heavens Four-Dimensional N=2(4) Superstring Backgrounds and The Real Heavens

1995-05-30

arxiv.org/abs/hep-th/9505177v1

Int.J.Mod.Phys. A11 (1996) 1279-1298

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, plain tex

Scientific paper

We study N=2(4) superstring backgrounds which are four-dimensional non-\Kahlerian 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 hyper-\Kahler Taub-NUT instanton background. It is shown that the integrable property of the non-\Kahlerian spaces have the direct origin in the real heavens: real, self-dual, euclidean, Einstein spaces. The Laplace equation and the continual Toda equation imposed on quasi-\Kahler geometry for consistent string propagation are related to the self-duality conditions of the real heavens with ``translational'' and ``rotational''Killing symmetry respectively.

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