Chern-Simons action and the Carrollian Cotton tensors
arXiv:2310.19929 · doi:10.1007/JHEP12(2023)130
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.
v1: 1+21 pages, Latex, v2: JHEP version
References in corpus (24)
- Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
- Conformal Carroll groups and BMS symmetry
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Setting the boundary free in AdS/CFT
- Carrollian Perspective on Celestial Holography
- Conformal Carroll groups
- Bridging Carrollian and Celestial Holography
- Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
- Field Theories with Conformal Carrollian Symmetry
- Carroll Expansion of General Relativity
- Conformal Carroll Scalars with Boosts
- On Higher-dimensional Carrollian and Galilean Conformal Field Theories
- Magnetic Carrollian gravity from the Carroll algebra
- Carrollian manifolds and null infinity: A view from Cartan geometry
- AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
- Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
- Energy-momentum/Cotton tensor duality for AdS4 black holes
- Flat from anti-de Sitter
- Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary
- Constructing Carrollian CFTs
- AdS supergravity, holography and Ward identities
- Ehlers, Carroll, Charges and Dual Charges
- Holography from Singular Supertranslations on a Black Hole Horizon
- Singular Supertranslations and Chern-Simons Theory on the Black Hole Horizon