Conformal Carroll groups

TL;DR

The paper develops a systematic family of infinite-dimensional conformal Carroll groups CCarr_k(d+1) labeled by an integer k, mirroring the conformal Galilei program and grounded in Carroll geometry. It shows how these symmetries arise from dual Newton–Cartan/Bargmann pictures, recover BMS and NU groups as special cases, and organize massless Carrollian models as strings in Bargmann space. By examining massless and massive representations via coadjoint orbits and Schild's null strings, the work establishes concrete links between Carrollian and Bargmann formalisms and exposes a rich hierarchy of finite- and infinite-dimensional symmetry algebras. The results illuminate geometric unification across NC, Carroll, and Bargmann frameworks and provide a conceptual bridge to asymptotic symmetries in gravity through BMS/NU structures.

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.