On certain Kähler quotients of quaternionic Kähler manifolds

V. Cortés (1) , J. Louis (2) , P. Smyth (3) , H. Triendl (4)

1 Department Mathematik
2 UHH - Universität Hamburg
3 EPFL - Ecole Polytechnique Fédérale de Lausanne
4 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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

Domains: Differential Geometry [math.DG]; High Energy Physics - Theory [hep-th]

V. Cortés, J. Louis, P. Smyth, H. Triendl. On certain Kähler quotients of quaternionic Kähler manifolds. Communications in Mathematical Physics, 2013, 317, pp.787-816. ⟨cea-00823343⟩