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Special geometry of Euclidean supersymmetry II: hypermultiplets and the c-map

Vicente Cortes·Christoph Mayer·Thomas Mohaupt·Frank Saueressig
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Abstract

We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N =2 supersymmetry. While the Minkowskian para-c-map is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, the Euclidean para-c-map corresponds to the dimensional reduction of the Euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are para-hyper-Kahler manifolds. We review and prove the relevant results of para-complex and para-hypercomplex geometry. In particular, we give a second, purely geometrical construction of both c-maps, by proving that the cotangent bundle N=T^*M of any affine special (para-)Kahler manifold M is para-hyper-Kahler.

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Vicente Cortes, Christoph Mayer, Thomas Mohaupt, Frank Saueressig. 2005-03-10. Special geometry of Euclidean supersymmetry II: hypermultiplets and the c-map. https://doi.org/10.1088/1126-6708%2F2005%2F06%2F025

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