Special geometry and space-time signature

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)-Kahler geometry. (C) 2017 The Author(s). Published by Elsevier B.V.