A construction that obtains three-dimensional AdS-Carroll and Carroll-Galilei Chern-Simons gravity theories by applying the Lie algebra expansion method to the 2D Euclidean AdS algebra and its flat version, rather than by contracting a 3D relativistic algebra. It exhibits the duality that the vanishing-cosmological-constant limit in 2D becomes a non-relativistic limit in 3D, cures the invariant-tensor degeneracy of the Carroll-Galilei sector with central extensions (Medina-Revoy theorem), and extends to Post-Carroll-Newtonian algebras.
This hep-th paper derives three-dimensional Carrollian (ultra-relativistic) gravity theories by applying the Lie algebra expansion method to two-dimensional Euclidean symmetry algebras. Starting from…