Hyperkahler Cones and Orthogonal Wolf Spaces

Details Hyperkahler Cones and Orthogonal Wolf Spaces Hyperkahler Cones and Orthogonal Wolf Spaces

2002-02-21

arxiv.org/abs/hep-th/0202149v2

JHEP 0205 (2002) 064

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex, 2 figures (references added)

Scientific paper

10.1088/1126-6708/2002/05/064

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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