On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions

Abstract

In this paper, we find a class of Carrollian and Galilean contractions of (extended) Bondi–van der Burg–Metzner–Sachs (BMS) algebra in 3+1 and 2+1 dimensions. To this end, we investigate possible embeddings of 3D/4D Poincaré into the BMS and BMS algebras, respectively. The contraction limits in the 2+1-dimensional case are then enforced by appropriate contractions of its Poincaré subalgebras. In 3+1 dimensions, we have to apply instead the analogy between the structures of Poincaré and BMS algebra. In the case of non-vanishing cosmological constant in 2+1 dimensions, we consider the contractions of Λ-BMS algebra in an analogous manner. As a by-product, we have also analyzed reality conditions on the Witt algebra and obtained new results.