On the Hyperkähler/Quaternion Kähler Correspondence

By N. Hitchin. 2012

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A hyperkähler manifold with a circle action fixing just one complex structure admits a natural hyperholomorphic line bundle. This observation forms the basis for the construction of a corresponding quaternionic Kähler manifold in the work of A.Haydys. In this paper the corresponding holomorphic line bundle on twistor space is described and many examples computed, including monopole and Higgs bundle moduli spaces. Finally a twistor version of the hyperkähler/quaternion Kähler correspondence is established.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ab37f45aa168b068432d459bba75bd52ef23e600