Linear perturbations of Hyperkahler metrics

Details Linear perturbations of Hyperkahler metrics Linear perturbations of Hyperkahler metrics

2008-06-27

arxiv.org/abs/0806.4620v4

Lett.Math.Phys.87:225-265,2009

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, 2 figures, uses JHEP3.cls; v4: section 5.3 shortened, matches published version

Scientific paper

10.1007/s11005-009-0305-8

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 arXiv:0810.1675, we extend these techniques to quaternionic-Kahler spaces with isometries.

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