HAL : hal-00328291, version 1
 arXiv : 0810.1675
 Communications in Mathematical Physics 296, 2 (2010) 353
 Linear perturbations of quaternionic metrics
 (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.
 Domaine : Physique/Physique des Hautes Energies - Théorie
 Mots Clés : High Energy Physics - Theory – Mathematics - Differential Geometry
 Lien vers le texte intégral : http://fr.arXiv.org/abs/0810.1675
 hal-00328291, version 1 http://hal.archives-ouvertes.fr/hal-00328291 oai:hal.archives-ouvertes.fr:hal-00328291 Contributeur : Boris Pioline <> Soumis le : Vendredi 10 Octobre 2008, 09:03:09 Dernière modification le : Dimanche 4 Avril 2010, 09:28:45