A twistor sphere of generalized Kahler potentials on hyperkahler manifolds
We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkah...
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ftdatacite:10.48550/arxiv.1111.3893 2023-05-15T15:03:10+02:00 A twistor sphere of generalized Kahler potentials on hyperkahler manifolds Dyckmanns, Malte 2011 https://dx.doi.org/10.48550/arxiv.1111.3893 https://arxiv.org/abs/1111.3893 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ High Energy Physics - Theory hep-th Differential Geometry math.DG FOS Physical sciences FOS Mathematics Preprint Article article CreativeWork 2011 ftdatacite https://doi.org/10.48550/arxiv.1111.3893 2022-04-01T13:54:13Z We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose description in projective superspace is fully understood. We use this relation to determine an S^2-family of generalized Kahler potentials for Euclidean space and for the Eguchi-Hanson geometry. Cotangent bundles of Hermitian symmetric spaces constitute a class of hyperkahler manifolds where our method can be applied immediately since the necessary results from projective superspace are already available. As a non-trivial higher-dimensional example, we determine the generalized potential for T*CP^n, which generalizes the Eguchi-Hanson result. : 17 pages. v2: Clarified references; improved appendix Report Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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High Energy Physics - Theory hep-th Differential Geometry math.DG FOS Physical sciences FOS Mathematics |
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High Energy Physics - Theory hep-th Differential Geometry math.DG FOS Physical sciences FOS Mathematics Dyckmanns, Malte A twistor sphere of generalized Kahler potentials on hyperkahler manifolds |
topic_facet |
High Energy Physics - Theory hep-th Differential Geometry math.DG FOS Physical sciences FOS Mathematics |
description |
We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose description in projective superspace is fully understood. We use this relation to determine an S^2-family of generalized Kahler potentials for Euclidean space and for the Eguchi-Hanson geometry. Cotangent bundles of Hermitian symmetric spaces constitute a class of hyperkahler manifolds where our method can be applied immediately since the necessary results from projective superspace are already available. As a non-trivial higher-dimensional example, we determine the generalized potential for T*CP^n, which generalizes the Eguchi-Hanson result. : 17 pages. v2: Clarified references; improved appendix |
format |
Report |
author |
Dyckmanns, Malte |
author_facet |
Dyckmanns, Malte |
author_sort |
Dyckmanns, Malte |
title |
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds |
title_short |
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds |
title_full |
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds |
title_fullStr |
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds |
title_full_unstemmed |
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds |
title_sort |
twistor sphere of generalized kahler potentials on hyperkahler manifolds |
publisher |
arXiv |
publishDate |
2011 |
url |
https://dx.doi.org/10.48550/arxiv.1111.3893 https://arxiv.org/abs/1111.3893 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1111.3893 |
_version_ |
1766335060707901440 |