Hyperkahler Cones and Orthogonal Wolf Spaces

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.

19 pages, Latex, 2 figures (references added)

References in corpus (2)

• Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry
• Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds

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