Characters of the BMS Group in Three Dimensions

TL;DR

The paper computes exact Frobenius-character expressions for the centrally extended BMS3 group by integrating over Virasoro coadjoint orbits and exploiting delta-function localization to bypass the ambiguities of functional measures. It yields mass- and vacuum-related characters that are independent of the detailed measure and valid for all positive central charges and constant supermomenta, revealing them as flat limits of Virasoro characters. The results connect BMS3 representation theory to high-energy Virasoro structures and suggest links to one-loop gravity partition functions in flat space, with potential extensions to higher spins and supersymmetric BMS3. This work thus clarifies the representation-theoretic underpinnings of BMS3 and provides concrete, computable character formulas for both massive particles and the vacuum sector.

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.