Chern-Simons action and the Carrollian Cotton tensors
Abstract In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2023)130 |
| _version_ | 1797233835974328320 |
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| author | Olivera Mišković Rodrigo Olea P. Marios Petropoulos David Rivera-Betancour Konstantinos Siampos |
| author_facet | Olivera Mišković Rodrigo Olea P. Marios Petropoulos David Rivera-Betancour Konstantinos Siampos |
| author_sort | Olivera Mišković |
| collection | DOAJ |
| description | Abstract In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated. |
| first_indexed | 2024-03-08T18:16:43Z |
| format | Article |
| id | doaj.art-867211bddf2946c8ae6917df448dd727 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T16:22:29Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-867211bddf2946c8ae6917df448dd7272024-03-31T11:08:44ZengSpringerOpenJournal of High Energy Physics1029-84792023-12-0120231212210.1007/JHEP12(2023)130Chern-Simons action and the Carrollian Cotton tensorsOlivera Mišković0Rodrigo Olea1P. Marios Petropoulos2David Rivera-Betancour3Konstantinos Siampos4Instituto de Física, Pontificia Universidad Católica de ValparaísoDepartamento de Ciencias Físicas, Universidad Andres BelloCentre de Physique Théorique — CPHT, Ecole Polytechnique, CNRS (Centre National de la Recherche Scientifique, Unité Mixte de Recherche UMR 7644), Institut Polytechnique de ParisCentre de Physique Théorique — CPHT, Ecole Polytechnique, CNRS (Centre National de la Recherche Scientifique, Unité Mixte de Recherche UMR 7644), Institut Polytechnique de ParisDepartment of Nuclear and Particle Physics, Faculty of Physics, National and Kapodistrian University of AthensAbstract In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated.https://doi.org/10.1007/JHEP12(2023)130Chern-Simons TheoriesClassical Theories of GravityHolography and Hydrodynamics |
| spellingShingle | Olivera Mišković Rodrigo Olea P. Marios Petropoulos David Rivera-Betancour Konstantinos Siampos Chern-Simons action and the Carrollian Cotton tensors Journal of High Energy Physics Chern-Simons Theories Classical Theories of Gravity Holography and Hydrodynamics |
| title | Chern-Simons action and the Carrollian Cotton tensors |
| title_full | Chern-Simons action and the Carrollian Cotton tensors |
| title_fullStr | Chern-Simons action and the Carrollian Cotton tensors |
| title_full_unstemmed | Chern-Simons action and the Carrollian Cotton tensors |
| title_short | Chern-Simons action and the Carrollian Cotton tensors |
| title_sort | chern simons action and the carrollian cotton tensors |
| topic | Chern-Simons Theories Classical Theories of Gravity Holography and Hydrodynamics |
| url | https://doi.org/10.1007/JHEP12(2023)130 |
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