Kleinian Geometry and the N=2 Superstring

Details Kleinian Geometry and the N=2 Superstring Kleinian Geometry and the N=2 Superstring

1993-02-16

arxiv.org/abs/hep-th/9302073v1

Int.J.Mod.Phys.A9:1457-1494,1994

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, AMS-TeX

Scientific paper

10.1142/S0217751X94000650

This paper is devoted to the exploration of some of the geometrical issues raised by the $N=2$ superstring. We begin by reviewing the reasons that $\beta$-functions for the $N=2$ superstring require it to live in a four-dimensional self-dual spacetime of signature $(--++)$, together with some of the arguments as to why the only degree of freedom in the theory is that described by the gravitational field. We then move on to describe at length the geometry of flat space, and how a real version of twistor theory is relevant to it. We then describe some of the more complicated spacetimes that satisfy the $\beta$-function equations. Finally we speculate on the deeper significance of some of these spacetimes.

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