Conformal Carroll groups

Abstract

Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled 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.

31 pages, no figures. Minor misprints corrected and clarifications added. To be published in J. Phys. A

References in corpus (3)

• The BMS/GCA correspondence
• Galilean Conformal Algebras and AdS/CFT
• Galilean Isometries

Cited by in corpus (5)

• Field Theories with Conformal Carrollian Symmetry
• Geometric actions for three-dimensional gravity
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Infinite towers of supertranslation and superrotation memories
• Addendum to "Super-GCA from $\mathcal{N}=(2,2)$ super-Virasoro": Super-GCA connection with tensionless strings