Gauging the Heisenberg algebra of special quaternionic manifolds

TL;DR

This paper investigates conditions under which certain abelian algebras can be gauged in N=2 supergravity with special quaternionic manifolds, extending known half-flatness conditions and exploring non-abelian generalizations.

Contribution

It identifies specific charge vector conditions enabling gauging of abelian algebras in N=2 supergravity and generalizes the half-flatness condition for Calabi-Yau compactifications.

Findings

Gauging is possible when symplectic charge vectors have vanishing scalar product.

The work extends half-flatness conditions in Calabi-Yau compactifications.

Discusses non-abelian extensions and their consistency.

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.