6D interpretation of 3D gravity
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 construct...
| Main Authors: | , , |
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| Format: | Article |
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IOP Publishing
2017
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| Online Access: | https://eprints.nottingham.ac.uk/42669/ |
| _version_ | 1848796541113860096 |
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| author | Herfray, Yannick Krasnov, Kirill Scarinci, Carlos |
| author_facet | Herfray, Yannick Krasnov, Kirill Scarinci, Carlos |
| author_sort | Herfray, Yannick |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:49:37Z |
| format | Article |
| id | nottingham-42669 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:49:37Z |
| publishDate | 2017 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-426692020-05-04T18:29:38Z https://eprints.nottingham.ac.uk/42669/ 6D interpretation of 3D gravity Herfray, Yannick Krasnov, Kirill Scarinci, Carlos 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. IOP Publishing 2017-01-24 Article PeerReviewed Herfray, Yannick, Krasnov, Kirill and Scarinci, Carlos (2017) 6D interpretation of 3D gravity. Classical and Quantum Gravity, 34 (4). ISSN 1361-6382 https://doi.org/10.1088/1361-6382/aa5727 doi:10.1088/1361-6382/aa5727 doi:10.1088/1361-6382/aa5727 |
| spellingShingle | Herfray, Yannick Krasnov, Kirill Scarinci, Carlos 6D interpretation of 3D gravity |
| title | 6D interpretation of 3D gravity |
| title_full | 6D interpretation of 3D gravity |
| title_fullStr | 6D interpretation of 3D gravity |
| title_full_unstemmed | 6D interpretation of 3D gravity |
| title_short | 6D interpretation of 3D gravity |
| title_sort | 6d interpretation of 3d gravity |
| url | https://eprints.nottingham.ac.uk/42669/ https://eprints.nottingham.ac.uk/42669/ https://eprints.nottingham.ac.uk/42669/ |