Special Geometry and Space-time Signature

Abstract

We construct N=2 four and five-dimensional supergravity theories coupled to vector multiplets in various space-time signatures (t,s), where t and s refer, respectively, to the number of time and spatial dimensions. The five-dimensional supergravity theories, t+s=5, are constructed by investigating the integrability conditions arising from Killing spinor equations. The five-dimensional supergravity theories can also be obtained by reducing Hull's eleven-dimensional supergravities on a Calabi-Yau threefold. The dimensional reductions of the five-dimensional supergravities on space and time-like circles produce N=2 four-dimensional supergravity theories with signatures (t-1,s) and (t,s-1) exhibiting projective special (para)-Kähler geometry.

13 pages

References in corpus (4)

• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• Pseudo-Riemannian VSI spaces II
• Pseudo-Riemannian VSI spaces
• Euclidean Supergravity and Multi-Centered Solutions

Cited by in corpus (1)

• Supersymmetry algebras in arbitrary signature and their R-symmetry groups