Twistor spaces for HKT manifolds

Details Twistor spaces for HKT manifolds Twistor spaces for HKT manifolds

1996-02-20

arxiv.org/abs/hep-th/9602108v1

Phys.Lett.B379:80-86,1996

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Phyzzx

Scientific paper

10.1016/0370-2693(96)00393-0

We construct the twistor space associated with an HKT manifold, that is, a hyper-K\"ahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifold. We also show how the metric and torsion of the HKT manifold can be determined from data on the twistor space by a reconstruction theorem. We give a geometric description of the sigma model (4,0) superfields as holomorphic maps (suitably understood) from a twistorial extension of (4,0) superspace (harmonic superspace) into the twistor space of the sigma model target manifold and write an action for the sigma model in terms of these (4,0) superfields.

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