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6D interpretation of 3D gravity

Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos

Authors

Yannick Herfray

KIRILL KRASNOV kirill.krasnov@nottingham.ac.uk
Professor of Mathematical Sciences

Carlos Scarinci



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.

Citation

Herfray, Y., Krasnov, K., & Scarinci, C. (2017). 6D interpretation of 3D gravity. Classical and Quantum Gravity, 34(4), https://doi.org/10.1088/1361-6382/aa5727

Journal Article Type Article
Acceptance Date Jan 3, 2017
Publication Date Jan 24, 2017
Deposit Date May 9, 2017
Publicly Available Date Mar 29, 2024
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 34
Issue 4
DOI https://doi.org/10.1088/1361-6382/aa5727
Public URL https://nottingham-repository.worktribe.com/output/839132
Publisher URL https://doi.org/10.1088/1361-6382/aa5727