A particle with torsion or a particle in AdS3 in 2+1 dimensions: teleparallel ideas at work

Abstract: We construct relativistic point-particle actions in 2+1 dimensions using the non-linear realisation (coset) approach for the Mielke–Baekler (MB) algebra. In the torsional branch (p=0) the same background admits two equivalent Cartan descriptions: a teleparallel formulation with a flat (curvature-free) Weitzenböck connection and constant torsion, and a torsionless formulation in which the induced metric is locally AdS3. We show explicitly how the worldline equations can be written either as parallel transport with respect to the torsionful teleparallel connection or, in the torsionless split, as geodesic motion supplemented by the standard spin–curvature coupling in the spinning case, Papapetrou like equation. Finally, we take the Carroll contraction of the MB particle and obtain the corresponding torsional Carroll dynamics.