Linear perturbations of quaternionic metrics

Details Linear perturbations of quaternionic metrics Linear perturbations of quaternionic metrics

2008-10-09

arxiv.org/abs/0810.1675v3

Commun.Math.Phys.296:353-403,2010

Physics

High Energy Physics

High Energy Physics - Theory

55 pages, 1 figure, uses JHEP3.cls; v2: one ref added, minor improvements; v3: title changed, sections 2.5 and 5.2 rewritten i

Scientific paper

10.1007/s00220-010-1022-y

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.

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