On the Hyperkähler/Quaternion Kähler Correspondence

Author: 

Hitchin, N

Publication Date: 

22 November 2013

Journal: 

Communications in Mathematical Physics

Last Updated: 

2020-01-16T22:16:21.673+00:00

Issue: 

1

Volume: 

324

DOI: 

10.1007/s00220-013-1689-y

page: 

77-106

abstract: 

A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of A.Haydys. We construct in this paper the corresponding holomorphic line bundle on twistor space and compute many examples, including monopole and Higgs bundle moduli spaces. We also show that the bundle on twistor space has a natural meromorphic connection which realizes it as the quantum line bundle for the hyperkaehler family of holomorphic symplectic structures. Finally we give a twistor version of the HK/QK correspondence.

Symplectic id: 

354527

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article