Gauging the Heisenberg algebra of special quaternionic manifolds

Abstract

We show that in N=2 supergravity, with a special quaternionic manifold of (quaternionic) dimension h_1+1 and in the presence of h_2 vector multiplets, a h_2+1 dimensional abelian algebra, intersecting the 2h_1+3 dimensional Heisenberg algebra of quaternionic isometries, can be gauged provided the h_2+1 symplectic charge--vectors V_I, have vanishing symplectic invariant scalar product V_I X V_J=0. For compactifications on Calabi--Yau three--folds with Hodge numbers (h_1,h_2) 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.