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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Main Author: Dyckmanns, Malte
Format: Report
Language:unknown
Published: arXiv 2011
Subjects:
High Energy Physics - Theory hep-th
Differential Geometry math.DG
FOS Physical sciences
FOS Mathematics
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.1111.3893
https://arxiv.org/abs/1111.3893
id ftdatacite:10.48550/arxiv.1111.3893
record_format openpolar
spelling 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
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic High Energy Physics - Theory hep-th
Differential Geometry math.DG
FOS Physical sciences
FOS Mathematics
spellingShingle 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

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