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 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...

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Bibliographic Details
Published in:Communications in mathematical physics 2013-02, Vol.317 (3), p.787-816
Main Authors: Cortés, V., Louis, J., Smyth, P., Triendl, H.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Differential Geometry
High Energy Physics - Theory
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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 to supersymmetry breaking.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-012-1541-9