Notes on the BMS group in three dimensions: I. Induced representations

Abstract

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.

Entanglement entropy in flat holography

“…Interesting developments include connections with Virasoro algebra [34], isomorphism between BMS algebra and Galileo conformal algebra [25], representations and bootstrap [37][38][39][40][41][42][43][44][45]. Flat holography based on BMS 3 symmetry was proposed in [25,26] and supporting evidence can be found in [46][47][48].…”

Flat holography: aspects of the dual field theory

“…• Induced representations [49,55,56]. The above checks of the holographic principle in flat space assumed that for holographic considerations, one needed to use highest weight representations of the underlying algebra.…”

“…But the problem with these highest weight conditions is that the representations are generically non-unitary. Explicitly unitary representations of the BMS algebra have been considered and these are induced representations constructed in [49,55]. They also have been recently constructed in the limit from AdS in [56].…”

Near-horizon BMS symmetries as fluid symmetries

“…In three spacetime dimensions, the BMS group has the form Diff(S 1 ) vir, where vir is the Virasoro algebra with central charge c = 3/G. The charge algebra arises from a Lie-Poisson bracket [25,26] and the boundary dynamics has a simple description [27][28][29]. We will study the fluid interpretation of 3d flat gravity in a companion paper [30].…”