Analysis reveals the vacuum character of BMS algebra mirrors a 1-loop partition function, suggesting insights into holography.
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 vacuum character of BMS₃ exactly agrees with the 1-loop partition function of three-dimensional asymptotic flat gravity. We expect the vacuum character of BMS₄ may shed light on the flat holography in four dimensions.
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Chen et al. (2025) studied this question.
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