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

TL;DR

This paper studies the highest weight representations of BMS algebra on codimension-two boundaries, revealing their structure, characters, and connections to flat holography and gravity partition functions.

Contribution

It constructs highest-weight BMS modules in 3D and 4D, computes their characters, and links the 3D vacuum character to flat gravity partition functions.

Findings

BMS$_3$ vacuum character matches 1-loop gravity partition function

Constructed highest-weight modules for BMS algebra in 3D and 4D

Insights into flat holography from character analysis

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.