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arXiv · 2507.10137

Character of the highest weight module of BMS algebra realized on codimensional-two boundary

Bin Chen·Song He·Pujian Mao·Xin-Cheng Mao
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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$_3$ 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 ``$i$''. We expect the vacuum character of BMS$_4$ may shed light on the flat holography in four dimensions.

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Bin Chen, Song He, Pujian Mao, Xin-Cheng Mao. 2025-07-14. Character of the highest weight module of BMS algebra realized on codimensional-two boundary. https://doi.org/10.1007/jhep01(2026)051

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