Abstract

We construct the hyperk¨ahler cones corresponding to the quaternion-K¨ahler
orthogonal Wolf spaces SO(n+4)/
SO(n)×SO(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 hyperk¨ahler potential, which we
compute from an SU(2) hyperk¨ahler quotient of flat space. We derive the
Killing vectors
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