Heterotic geometry without isometries

Details Heterotic geometry without isometries Heterotic geometry without isometries

2005-08-15

arxiv.org/abs/hep-th/0508106v2

JHEP 0510 (2005) 061

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, no figures, english corrected and some references added

Scientific paper

10.1088/1126-6708/2005/10/061

We present some properties of hyperkahler torsion (or heterotic) geometry in four dimensions that make it even more tractable than its hyperkahler counterpart. We show that in $d=4$ hypercomplex structures and weak torsion hyperkahler geometries are the same. We present two equivalent formalisms describing such spaces, they are stated in the propositions of section 1. The first is reduced to solve a non-linear system for a doublet of potential functions, first found by Plebanski and Finley. The second is equivalent to finding the solutions of a quadratic Ashtekar-Jacobson-Smolin like system, but without a volume preserving condition. This is why heterotic spaces are simpler than usual hyperkahler ones. We also analyze the strong version of this geometry. Certain examples are presented, some of them are metrics of the Callan-Harvey-Strominger type and others are not. In the conclusion we discuss the benefits and disadvantages of both formulations in detail.

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