%0 Journal Article
%T Linear perturbations of Hyperkahler metrics
%+ Laboratoire de Physique Théorique et Astroparticules (LPTA)
%+ Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
%+ Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS)
%+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT)
%+ Institute for Theoretical Physics [Utrecht]
%A Alexandrov, Sergei
%A Pioline, Boris
%A Saueressig, Frank
%A Vandoren, Stefan
%Z 44 pages, 2 figures, uses JHEP3.cls
%< avec comité de lecture
%@ 0377-9017
%J Letters in Mathematical Physics
%I Springer Verlag
%V 87
%N 3
%P 225
%8 2009
%D 2009
%Z 0806.4620
%R 10.1007/s11005-009-0305-8
%Z Physics [physics]/High Energy Physics - Theory [hep-th]Journal articles
%X 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.
%G English
%L hal-00292412
%U https://hal.science/hal-00292412
%~ IN2P3
%~ CEA
%~ UNIV-PARIS7
%~ ENS-PARIS
%~ UPMC
%~ LPTA
%~ CNRS
%~ LPTENS
%~ LPTHE
%~ UNIV-MONTP2
%~ DSM-IPHT
%~ PSL
%~ UPMC_POLE_2
%~ UNIV-MONTPELLIER
%~ CEA-DRF
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UNIV-PARIS
%~ UP-SCIENCES
%~ ENS-PSL
%~ SU-TI
%~ ANR
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE
%~ ALLIANCE-SU
%~ UM1-UM2