Characters of the BMS Group in Three Dimensions

TL;DR

This paper computes exact characters of the BMS$_3$ group representations using a functional integral approach, revealing results independent of measure details and connecting to Virasoro characters in the flat limit.

Contribution

It introduces a novel exact character calculation for BMS$_3$ representations via coadjoint orbit integrals, extending the understanding of BMS symmetries in three dimensions.

Findings

Exact character formulas for BMS$_3$ group derived

Results are measure-independent and valid for all central charges

Connections established between BMS$_3$ and Virasoro characters

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.