%0 Journal Article
%T Linear perturbations of quaternionic metrics
%+ Laboratoire de Physique Théorique et Astroparticules (LPTA)
%+ Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
%+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT)
%+ Institute for Theoretical Physics [Utrecht]
%A Alexandrov, Sergey
%A Pioline, Boris
%A Saueressig, Frank
%A Vandoren, Stefan
%Z MRTN-CT-2004-005104
%Z 55 pages, 1 figure, uses JHEP3.cls
%< avec comité de lecture
%Z 08-054
%@ 0010-3616
%J Communications in Mathematical Physics
%I Springer Verlag
%V 296
%N 2
%P 353-403
%8 2010
%D 2010
%Z 0810.1675
%R 10.1007/s00220-010-1022-y
%K High Energy Physics
%K Theory
%K Mathematics
%K Differential Geometry
%Z Physics [physics]/High Energy Physics - Theory [hep-th]Journal articles
%X 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.
%G English
%L hal-00328291
%U https://hal.science/hal-00328291
%~ IN2P3
%~ CEA
%~ UNIV-PARIS7
%~ UPMC
%~ LPTA
%~ CNRS
%~ LPTHE
%~ UNIV-MONTP2
%~ DSM-IPHT
%~ UPMC_POLE_2
%~ UNIV-MONTPELLIER
%~ CEA-DRF
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UNIV-PARIS
%~ SU-TI
%~ ANR
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE
%~ ALLIANCE-SU
%~ UM1-UM2