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Letters in Mathematical Physics 87, 3 (2009) 225
Linear perturbations of Hyperkahler metrics
Sergei Alexandrov1, Boris Pioline2, 3, Frank Saueressig4, Stefan Vandoren5
(2009)

We study general linear perturbations of a class of 4d real-dimensional hyperkahler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic functions of 2d+1 variables, as opposed to the functions of d+1 variables controlling the unperturbed metric. Such deformations generically break all tri-holomorphic isometries of the unperturbed metric. Geometrically, these functions generate the symplectomorphisms which relate local complex Darboux coordinate systems in different patches of the twistor space. The deformed Kahler potential follows from these data by a Penrose-type transform. As an illustration of our general framework, we determine the leading exponential deviation of the Atiyah-Hitchin manifold away from its negative mass Taub-NUT limit. In a companion paper, we extend these techniques to quaternionic-Kahler spaces with isometries.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
2 :  LPTHE - Laboratoire de Physique Théorique et Hautes Energies
3 :  LPTENS - Laboratoire de Physique Théorique de l'ENS
4 :  IPHT - Institut de Physique Théorique (ex SPhT)
5 :  Institute for Theoretical Physics and Spinoza Institute
Physique/Physique des Hautes Energies - Théorie
Lien vers le texte intégral : 
http://fr.arXiv.org/abs/0806.4620