A geometrical invitation to BMS group theory

TL;DR

This paper provides a geometric and group-theoretical framework for understanding BMS symmetries at null infinity, emphasizing their structure and representations without relying on bulk spacetime realization.

Contribution

It introduces a purely geometric and group-theoretical approach to BMS symmetries, clarifying their structure and relation to Minkowski spacetime in any dimension.

Findings

Defines BMS transformations as conformal Carrollian isometries

Explores the semidirect structure of the BMS group

Connects good cuts to Poincaré subgroups and vacua

Abstract

In these lecture notes, a group-theoretical introduction to BMS symmetries is provided in a self-contained manner. More precisely, all definitions and structures are purely based on geometrical and group-theoretical notions defined at null infinity and valid in any dimension, in a way that circumvents its traditional bulk realisation as asymptotic symmetries. The topics which are reviewed are: the definition of BMS transformations as conformal Carrollian isometries of null infinity, the semidirect structure of the BMS group, the holographic reconstruction of Minkowski spacetime in terms of good cuts, the one-to-one correspondence between good cut subspaces and Poincar\'e subgroups (aka vacua), as well as a basic introduction to unitary representations of the BMS group.