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.
Keywords
Cite
@article{arxiv.hep-th/0202149,
title = {Hyperkahler Cones and Orthogonal Wolf Spaces},
author = {Lilia Anguelova and Martin Rocek and Stefan Vandoren},
journal= {arXiv preprint arXiv:hep-th/0202149},
year = {2009}
}
Comments
19 pages, Latex, 2 figures (references added)