Work

A 4D gravity theory and $G_2$-holonomy manifolds

Year: 2018

Type: article

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.

Source: Advances in Theoretical and Mathematical Physics

DOI: 10.4310/atmp.2018.v22.n8.a5

Authors: Yannick Herfray, Kirill Krasnov, Carlos Scarinci, Yuri Shtanov

Institutions: Université Libre de Bruxelles, University of Nottingham, Korea Institute for Advanced Study, Bogolyubov Institute for Theoretical Physics

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: State Fund for Fundamental Research of Ukraine, Science and Technology Facilities Council

Award: G7934480667