A 4D gravity theory and G2-holonomy manifolds

Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos; Shtanov, Yuri

Abstract

© 2019 International Press of Boston, Inc. 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 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 di_eomorphism-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.

Citation

Herfray, Y., Krasnov, K., Scarinci, C., & Shtanov, Y. (2019). A 4D gravity theory and G2-holonomy manifolds. Advances in Theoretical and Mathematical Physics, 22(8), 2001-2034. https://doi.org/10.4310/ATMP.2018.v22.n8.a5

• Journal Article Type: Article
• Acceptance Date: Jul 3, 2019
• Online Publication Date: Jul 18, 2019
• Publication Date: Jul 18, 2019
• Deposit Date: Jul 19, 2019
• Publicly Available Date: Jul 19, 2019
• Journal: Advances in Theoretical and Mathematical Physics
• Print ISSN: 1095-0761
• Electronic ISSN: 1095-0753
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Issue: 8
• Pages: 2001-2034
• DOI: https://doi.org/10.4310/ATMP.2018.v22.n8.a5
• Keywords: General physics and astronomy; General mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/2321466
• Publisher URL: https://intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0022/0008/a005/index.html
• Contract Date: Jul 19, 2019