Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-06-17
Class.Quant.Grav.20:4239-4268,2003
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 41 pages, 2 figures
Scientific paper
10.1088/0264-9381/20/19/308
We construct explicit cohomogeneity two metrics of G_2 holonomy, which are foliated by twistor spaces. The twistor spaces are S^2 bundles over four-dimensional Bianchi IX Einstein metrics with self-dual (or anti-self-dual) Weyl tensor. Generically the 4-metric is of triaxial Bianchi IX type, with SU(2) isometry. We derive the first-order differential equations for the metric coefficients, and obtain the corresponding superpotential governing the equations of motion, in the general triaxial Bianchi IX case. In general our metrics have singularities, which are of orbifold or cosmic-string type. For the special case of biaxial Bianchi IX metrics, we give a complete analysis their local and global properties, and the singularities. In the triaxial case we find that a system of equations written down by Tod and Hitchin satisfies our first-order equations. The converse is not always true. A discussion is given of the possible implications of the singularity structure of these spaces for M-theory dynamics.
Cvetic Mirjam
Gibbons Gary W.
Lu Hai
Pope Christopher N.
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