6D Interpretation of 3D Gravity. (24th January 2017)

• Record Type: Journal Article
• Authors: Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
• Is Part Of: Classical and quantum gravity. Volume 34:Number 4(2017:Feb.)
• Publication Date: 2017-01-24
• Subjects: 3D gravity -- pure connection description of gravity -- Hitchin theory; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/aa5727
• Languages: English
• ISSNs: 0264-9381

Abstract

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 S U ( 2 ) invariant closed 3-form in the total space of the principal S U ( 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.