On Certain Kähler Quotients of Quaternionic Kähler Manifolds

We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kahler manifold M which preserves a submanifold N ⊂ M, the quotient M′ = N/A has a natural Kahler structure. We verify that the assumptions on the group action and on the submanifold N ⊂ M are satisfied for a large class of examples obtained from the supergravity c-map. In particular, we find that all quaternionic Kahler manifolds M in the image of the c-map admit an integrable complex structure compatible with the quaternionic structure, such that N ⊂ M is a complex submanifold. Finally, we discuss how the existence of the Kahler structure on M′ is required by the consistency of spontaneous \({\mathcal{N} = 2}\) to \({\mathcal{N} = 1}\) supersymmetry breaking.