Conformal Carroll groups

Conformal extensions of Lévy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k . This framework includes and extends our recent study of the Bondi–Metzner–Sachs (BMS) and Newman–Unti (NU) groups. The relation to conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by ‘Carrollian photons’. Motion both in the Newton–Cartan and Carroll spaces may be related to that of strings in the Bargmann space.