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Journal Articles Communications in Mathematical Physics Year : 2013

On certain Kähler quotients of quaternionic Kähler manifolds

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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 $N \subset M$, 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.
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Dates and versions

cea-00823343 , version 1 (13-01-2021)

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Cite

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⟩
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