Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry

Details Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry

2004-11-18

arxiv.org/abs/hep-th/0411165v2

J.Geom.Phys. 56 (2006) 2463-2479

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 2 figures, LaTeX2e, typos fixed, references and a note added

Scientific paper

We construct infinitely many seven-dimensional Einstein metrics of weak holonomy G_2. These metrics are defined on principal SO(3) bundles over four-dimensional Bianchi IX orbifolds with the Tod-Hitchin metrics. The Tod-Hitchin metric has an orbifold singularity parameterized by an integer, and is shown to be similar near the singularity to the Taub-NUT de Sitter metric with a special charge. We show, however, that the seven-dimensional metrics on the total space are actually smooth. The geodesics on the weak G_2 manifolds are discussed. It is shown that the geodesic equation is equivalent to the Hamiltonian equation of an interacting rigid body system. We also discuss M-theory on the product space of AdS_4 and the seven-dimensional manifolds, and the dual gauge theories in three-dimensions.

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