Time-like reductions of five-dimensional supergravity

Abstract

In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In both cases the scalar manifold of the reduced theory is described as an eight-dimensional Lie group $L$ (the Iwasawa subgroup of $G_{2(2)}$) with a left-invariant para-quaternionic-Kähler structure. We show that depending on whether one reduces first over space or over time, the group $L$ is mapped to two different open $L$-orbits on the pseudo-Riemannian symmetric space $G_{2(2)}/(SL(2)\cdot SL(2))$. These two orbits are inequivalent in the sense that they are distinguished by the existence of integrable $L$-invariant complex or para-complex structures.

41 pages. Minor revision: one reference and comments added

References in corpus (8)

• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Universal BPS structure of stationary supergravity solutions
• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• BPS Black Holes
• Subtracted Geometry From Harrison Transformations
• 5D Black Holes and Non-linear Sigma Models
• A General Black String and its Microscopics
• The symmetries of five-dimensional minimal supergravity reduced to three dimensions

Cited by in corpus (4)

• An Inverse Scattering Construction of the JMaRT Fuzzball
• A Riemann-Hilbert approach to rotating attractors
• Geroch Group Description of Bubbling Geometries
• Five-dimensional Nernst branes from special geometry