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Communications in Mathematical Physics 296, 2 (2010) 353
Linear perturbations of quaternionic metrics
Sergey Alexandrov1, Boris Pioline2, Frank Saueressig3, Stefan Vandoren4
(2010)

We extend the twistor methods developed in our earlier work on linear deformations of hyperkahler manifolds [arXiv:0806.4620] to the case of quaternionic-Kahler manifolds. Via Swann's construction, deformations of a 4d-dimensional quaternionic-Kahler manifold $M$ are in one-to-one correspondence with deformations of its $4d+4$-dimensional hyperkahler cone $S$. The latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space $Z_S$, with a suitable homogeneity condition that ensures that the hyperkahler cone property is preserved. Equivalently, we show that the deformations of $M$ can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space $Z_M$ of $M$, by-passing the Swann bundle and its twistor space. We specialize these general results to the case of quaternionic-Kahler metrics with $d+1$ commuting isometries, obtainable by the Legendre transform method, and linear deformations thereof. We illustrate our methods for the hypermultiplet moduli space in string theory compactifications at tree- and one-loop level.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
2 :  LPTHE - Laboratoire de Physique Théorique et Hautes Energies
3 :  IPHT - Institut de Physique Théorique (ex SPhT)
4 :  Institute for Theoretical Physics and Spinoza Institute
Physique/Physique des Hautes Energies - Théorie
High Energy Physics - Theory – Mathematics - Differential Geometry
Lien vers le texte intégral : 
http://fr.arXiv.org/abs/0810.1675