Twistor Spaces for QKT Manifolds

Details Twistor Spaces for QKT Manifolds Twistor Spaces for QKT Manifolds

1997-10-08

arxiv.org/abs/hep-th/9710072v1

Commun.Math.Phys.197:713-727,1998

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, phyzzx

Scientific paper

10.1007/s002200050469

We find that the target space of two-dimensional (4,0) supersymmetric sigma models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a quaternionic K\"ahler manifold with torsion. We give four examples of geodesically complete QKT manifolds one of which is a generalisation of the LeBrun geometry. We then construct the twistor space associated with a QKT manifold and show that under certain conditions it is a K\"ahler manifold with a complex contact structure. We also show that, for every 4k-dimensional QKT manifold, there is an associated 4(k+1)-dimensional hyper-K\"ahler one.

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