Gauging the Heisenberg algebra of special quaternionic manifolds
Abstract
We show that in N=2 supergravity, with a special quaternionic manifold of (quaternionic) dimension h1+1 and in the presence of h2 vector multiplets, a h2+1 dimensional abelian algebra, intersecting the 2h1+3 dimensional Heisenberg algebra of quaternionic isometries, can be gauged provided the h2+1 symplectic charge--vectors VI, have vanishing symplectic invariant scalar product VI X VJ=0. For compactifications on Calabi--Yau three--folds with Hodge numbers (h1,h2) such condition generalizes the half--flatness condition as used in the recent literature. We also discuss non--abelian extensions of the above gaugings and their consistency conditions.
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