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arXiv · hep-th/0608192

Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples

Gaston Giribet·Osvaldo P. Santillan
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Abstract

Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By considering the Apostolov-Salamon theorem math.DG/0303197, we construct a new example that, still being a T^2 bundle over hyper-Kahler, represents a non trivial two parameter deformation of the metrics studied in hep-th/0108191. We then review the Spin(7) metrics arising from a T^3 bundle over a hyper-Kahler and we find two parameter deformation of such spaces as well. We show that if the hyper-Kahler base satisfies certain properties, a non trivial three parameter deformations is also possible. The relation between these spaces with the half-flat structures and almost G_2 holonomy spaces is briefly discussed.

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Gaston Giribet, Osvaldo P. Santillan. 2007-04-18. Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples. https://doi.org/10.1007/s00220-007-0300-9

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