Chern-Simons action and the Carrollian Cotton tensors - Archive ouverte HAL
Article Dans Une Revue Journal of High Energy Physics Année : 2023

Chern-Simons action and the Carrollian Cotton tensors

Résumé

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.

Dates et versions

hal-04284094 , version 1 (14-11-2023)

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Citer

Olivera Miskovic, Rodrigo Olea, P. Marios Petropoulos, David Rivera-Betancour, Konstantinos Siampos. Chern-Simons action and the Carrollian Cotton tensors. Journal of High Energy Physics, 2023, 12, pp.130. ⟨10.1007/JHEP12(2023)130⟩. ⟨hal-04284094⟩
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