Special geometry of Euclidean supersymmetry IV: the local c-map

Open Access
Regular Article - Theoretical Physics


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.


Differential and Algebraic Geometry Supergravity Models 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • V. Cortés
    • 1
  • P. Dempster
    • 2
  • T. Mohaupt
    • 3
  • O. Vaughan
    • 1
  1. 1.Department of Mathematics and Center for Mathematical PhysicsUniversity of HamburgHamburgGermany
  2. 2.School of Physics & Astronomy and Center for Theoretical PhysicsSeoul National UniversitySeoulKorea
  3. 3.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolU.K.

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