Compact weak G_2-manifolds with conical singularities

Details Compact weak G_2-manifolds with conical singularities Compact weak G_2-manifolds with conical singularities

2003-02-04

arxiv.org/abs/hep-th/0302021v2

Nucl.Phys. B663 (2003) 343-364

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, Latex, version to be published in Nucl. Phys. B, minor changes, one appendix added

Scientific paper

10.1016/S0550-3213(03)00388-2

We construct 7-dimensional compact Einstein spaces with conical singularities that preserve 1/8 of the supersymmetries of M-theory. Mathematically they have weak G_2-holonomy. We show that for every non-compact G_2-holonomy manifold which is asymptotic to a cone on a 6-manifold Y, there is a corresponding weak G_2-manifold with two conical singularities which, close to the singularities, looks like a cone on Y. Our construction provides explicit metrics on these weak G_2-manifolds. We completely determine the cohomology of these manifolds in terms of the cohomology of Y.

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