Linear perturbations of quaternionic metrics

Abstract

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.

55 pages, 1 figure, uses JHEP3.cls; v2: one ref added, minor improvements; v3: title changed, sections 2.5 and 5.2 rewritten in part, ref [26] added

References in corpus (8)

• String loop corrected hypermultiplet moduli spaces
• 4D N = 2 Supergravity and Projective Superspace
• D-instantons and twistors
• Properties of hyperkahler manifolds and their twistor spaces
• On superconformal projective hypermultiplets
• Linear perturbations of Hyperkahler metrics
• Quantum covariant c-map
• Tensor supermultiplets and toric quaternion-Kahler geometry

Cited by in corpus (33)

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• $R^3$ index for four-dimensional $N=2$ field theories
• S-duality in Twistor Space
• Multiple D3-instantons and mock modular forms II
• On the topology of the hypermultiplet moduli space in type II/CY string vacua
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• Hypermultiplet metric and D-instantons
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• TBA for non-perturbative moduli spaces
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• Heterotic-type II duality in twistor space
• Heisenberg symmetry and hypermultiplet manifolds
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• c-map as c=1 string
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