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Twistor Spaces for QKT Manifolds
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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.
Forward citations
Cited by 2 Pith papers
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On the rigidity of special and exceptional geometries with torsion a closed $3$-form
Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
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Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces
Holomorphic, torsion-parallel vector fields on KT manifolds induce Killing and holomorphic vector fields on Hermitian-Einstein moduli spaces, which become toric or QKT fibrations under extra closure conditions.
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