NDLI: Linear Perturbations of Hyperkähler Metrics

Content Provider	Springer Nature Link
Author	Pioline, Boris Alexandrov, Sergei Vandoren, Stefan Saueressig, Frank
Copyright Year	2009
Abstract	We study general linear perturbations of a class of 4d real-dimensional hyperkähler 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 Kähler 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.
Ending Page	265
Page Count	41
Starting Page	225
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	3
Volume Number	87
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-02-26
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	twistor methods Geometry Twistor methods Mathematical and Computational Physics Hyper-KÃ¤hler and quaternionic KÃ¤hler geometry, ``special'' geometry Group Theory and Generalizations applications to physics hyperkähler geometry Statistical Physics Applications to physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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