6D interpretation of 3D gravity

Herfray, Yannick and Krasnov, Kirill and Scarinci, Carlos (2017) 6D interpretation of 3D gravity. Classical and Quantum Gravity, 34 (4). ISSN 1361-6382

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Abstract

We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern–Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets an explanation of why the pure connection formulation of 3D gravity exists. More generally, we interpret 3D gravity as the dimensional reduction of the 6D Hitchin theory. To this end, we show that any $\text{SU}(2)$ invariant closed 3-form in the total space of the principal $\text{SU}(2)$ bundle can be parametrised by a connection together with a 2-form field on the base. The dimensional reduction of the 6D Hitchin theory then gives rise to 3D gravity coupled to a topological 2-form field.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1088/1361-6382/aa5727
Depositing User: Eprints, Support
Date Deposited: 09 May 2017 12:10
Last Modified: 11 May 2017 04:14
URI: http://eprints.nottingham.ac.uk/id/eprint/42669

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