Character of the highest weight module of BMS algebra realized on codimensional-two boundary
Abstract
In this paper, we investigate the highest weight representation (HWR) of the three and four-dimensional Bondi-Metzner-Sachs (BMS) algebra realized on the codimension-two boundary of asymptotic flat spacetime (AFS). In such a realization, the action of supertranslation shifts the conformal weight of the highest-weight states. As a result, there is no extra quantum number relating to the supertranslation. We construct the highest-weight BMS modules and compute their characters. We show that the BMS highest-weight vacuum character with special value of central charges coincides with the 1-loop partition function of three-dimensional asymptotic flat gravity, up to an overall phase factor ``''. We expect the vacuum character of BMS may shed light on the flat holography in four dimensions.
Keywords
Cite
@article{arxiv.2507.10137,
title = {Character of the highest weight module of BMS algebra realized on codimensional-two boundary},
author = {Bin Chen and Song He and Pujian Mao and Xin-Cheng Mao},
journal= {arXiv preprint arXiv:2507.10137},
year = {2026}
}
Comments
v3: 1+30 pages, 1 figure, major revision, connections to induced representation clarified, to appear in JHEP