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arXiv · 1602.03428

A 4D gravity theory and G2-holonomy manifolds

Yannick Herfray·Kirill Krasnov·Carlos Scarinci·Yuri Shtanov
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Abstract

Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3) bundle (with fibers R^3) over a 4-dimensional base, with a connection on this bundle. We make essentially the same ansatz for the calibrating 3-form, but use the curvature 2-forms instead of the ASD ones. We show that the resulting 3-form defines a metric of G2 holonomy if the connection satisfies a certain second-order PDE. This is exactly the same PDE that arises as the field equation of a certain 4-dimensional gravity theory formulated as a diffeomorphism-invariant theory of SO(3) connections. Thus, every solution of this 4-dimensional gravity theory can be lifted to a G2-holonomy metric. Unlike all previously known constructions, the theory that we lift to 7 dimensions is not topological. Thus, our construction should give rise to many new metrics of G2 holonomy. We describe several examples that are of cohomogeneity one on the base.

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Yannick Herfray, Kirill Krasnov, Carlos Scarinci, Yuri Shtanov. 2016-02-10. A 4D gravity theory and G2-holonomy manifolds. https://doi.org/10.4310/atmp.2018.v22.n8.a5

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