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- Title
On Certain Kähler Quotients of Quaternionic Kähler Manifolds.
- Authors
Cortés, V.; Louis, J.; Smyth, P.; Triendl, H.
- Abstract
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 ⊂ 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 ⊂ 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 ⊂ M is a complex submanifold. Finally, we discuss how the existence of the Kähler structure on M′ is required by the consistency of spontaneous $${\mathcal{N} = 2}$$ to $${\mathcal{N} = 1}$$ supersymmetry breaking.
- Subjects
QUATERNIONS; MANIFOLDS (Mathematics); MATHEMATICAL proofs; ISOMETRICS (Mathematics); ABELIAN groups; SUBMANIFOLDS; SUPERSYMMETRY; SYMMETRY breaking
- Publication
Communications in Mathematical Physics, 2013, Vol 317, Issue 3, p787
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-012-1541-9