Characters of the BMS Group in Three Dimensions

Abstract

Using the Frobenius formula, we evaluate characters associated with certain induced representations of the centrally extended BMS${}_3$ group. This computation involves a functional integral over a coadjoint orbit of the Virasoro group; a delta function localizes the integral to a single point, allowing us to obtain an exact result. The latter is independent of the specific form of the functional measure, and holds for all values of the BMS${}_3$ central charges and all values of the chosen mass and spin. It can also be recovered as a flat limit of Virasoro characters.

22 pages. v2: Updated references [5], [7] and [45]. Published in Communications in Mathematical Physics. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-015-2408-7

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• Semi-classical BMS-blocks from the Oscillator Construction
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography