Abstract
We consider timelike and spacelike reductions of 4D, \( \mathcal{N}=2 \) Minkowskian and Euclidean vector multiplets coupled to supergravity and the maps induced on the scalar geometry. In particular, we investigate (i) the (standard) spatial c-map, (ii) the temporal c-map, which corresponds to the reduction of the Minkowskian theory over time, and (iii) the Euclidean c-map, which corresponds to the reduction of the Euclidean theory over space. In the last two cases we prove that the target manifold is para-quaternionic Kähler.
In cases (i) and (ii) we construct two integrable complex structures on the target manifold, one of which belongs to the quaternionic and para-quaternionic structure, respectively. In case (iii) we construct two integrable para-complex structures, one of which belongs to the para-quaternionic structure.
In addition we provide a new global construction of the spatial, temporal and Euclidean c-maps, and separately consider a description of the target manifold as a fibre bundle over a projective special Kähler or para-Kähler base.
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Cortés, V., Dempster, P., Mohaupt, T. et al. Special geometry of Euclidean supersymmetry IV: the local c-map. J. High Energ. Phys. 2015, 66 (2015). https://doi.org/10.1007/JHEP10(2015)066
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DOI: https://doi.org/10.1007/JHEP10(2015)066