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) BMS algebra in 3+1 and 2+1 dimensions. To this end, we investigate possible embeddings of 3D/4D Poincaré into the BMS${}_3$ and BMS${}_4$ 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 $\Lambda$-BMS${}_3$ algebra in an analogous manner.

14 pages, v2 the role of real forms clarified, extended discussion of the contractions of $\Lambda$-BMS_3, typos in formulae corrected, references added, v3 Introduction and Conclusions expanded, new remarks in Sections III and IV, references added

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