The Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the circle with the space of its adjoint representation, embedded as an abelian normal subgroup. The structure of the group suggests to study induced representations; we show here that they are associated with the well-known coadjoint orbits of the Virasoro group and provide explicit representations in terms of one-particle states.

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Abstract:The coadjoint representation of the BMS 3 group, which governs the covariant phase space of three-dimensional asymptotically flat gravity, is investigated. In particular, we classify coadjoint BMS 3 orbits and show that intrinsic angular momentum is free of supertranslation ambiguities. Finally, we discuss the link with induced representations upon geometric quantization.