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arXiv · hep-th/0202149

Hyperkahler Cones and Orthogonal Wolf Spaces

Lilia Anguelova·Martin Rocek·Stefan Vandoren
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Abstract

We construct the hyperkahler cones corresponding to the Quaternion-Kahler orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions, which appear in hypermultiplet couplings to N=2 supergravity. The geometry is completely encoded by a single function, the hyperkahler potential, which we compute from an SU(2) hyperkahler quotient of flat space. We derive the Killing vectors and moment maps for the SO(n+4) isometry group on the hyperkahler cone. For the non-compact case, the isometry group SO(n,4) contains n+2 abelian isometries which can be used to find a dual description in terms of n tensor multiplets and one double-tensor multiplet. Finally, using a representation of the hyperkahler quotient via quiver diagrams, we deduce the existence of a new eight dimensional ALE space.

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Lilia Anguelova, Martin Rocek, Stefan Vandoren. 2002-03-27. Hyperkahler Cones and Orthogonal Wolf Spaces. https://doi.org/10.1088/1126-6708%2F2002%2F05%2F064

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