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Twist Geometry of the c-Map

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Abstract

We discuss the geometry of the c-map from projective special Kähler to quaternionic Kähler manifolds using the twist construction to provide a global approach to Hitchin’s description. As found by Alexandrov et al. and Alekseevsky et al. this is related to the quaternionic flip of Haydys. We prove uniqueness statements for several steps of the construction. In particular, we show that, given a hyperKähler manifold with a rotating symmetry, there is essentially only a one parameter degree of freedom in constructing a quaternionic Kähler manifold of the same dimension. We demonstrate how examples on group manifolds arise from this picture.

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Authors and Affiliations

  1. Departamento de Geometria y Topologia, Facultad de Ciencias Matematicas, Universidad de Valencia, C. Dr Moliner, 50, 46100, Burjassot, Valencia, Spain

    Oscar Macia

  2. Department of Mathematics, Aarhus University, Ny Munkegade 118, Bldg 1530, 8000, Aarhus C, Denmark

    Andrew Swann

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  1. Oscar Macia
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  2. Andrew Swann
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Correspondence to Andrew Swann.

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Communicated by N. A. Nekrasov

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Macia, O., Swann, A. Twist Geometry of the c-Map. Commun. Math. Phys. 336, 1329–1357 (2015). https://doi.org/10.1007/s00220-015-2314-z

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  • DOI: https://doi.org/10.1007/s00220-015-2314-z

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