JHEP, 01, 051 (2026)
Character of the highest weight module of BMS algebra realized on codimensional-two boundary
Bin Chen1, 2, 3, Song He1, 5, Pujian Mao4 and Xin-Cheng Mao2
1 Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, China.
2 School of Physics, Peking University, No.5 Yiheyuan Rd, Beijing 100871, P. R. China.
3 Center for High Energy Physics, Peking University, No.5 Yiheyuan Rd, Beijing 100871, P. R. China.
4 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China.
5 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muhlenberg 1, 14476 Golm, Germany.
* chenbin1@nbu.edu.cn, hesong@nbu.edu.cn, pjmao@tju.edu.cn, maoxc1120@stu.pku.edu.cn
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 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.
