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<p>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<sub>3</sub> 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>i</i>”. We expect the vacuum character of BMS<sub>4</sub> may shed light on the flat holography in four dimensions.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月7日

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  • Bin Chen,
  • Song He,
  • Pujian Mao,
  • Xin-Cheng Mao

摘要

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 BMS3 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 BMS4 may shed light on the flat holography in four dimensions.