Coadjoint representation of the BMS group on celestial Riemann surfaces

TL;DR

This work constructs and analyzes the coadjoint representation of the four-dimensional BMS group on celestial Riemann surfaces, covering both the sphere and the punctured plane, and provides explicit structure constants for different bases.It develops a Weyl-covariant, two-dimensional geometric framework that unifies conformal fields and weighted scalars, enabling a detailed description of how the BMS4 algebra and group act on dual elements.The authors connect the coadjoint data to non-radiative gravitational data at null infinity via a moment map, and they lay out explicit expansions (spin-weighted harmonics and overcomplete bases) and transformation laws, preparing the ground for orbit classification and geometric quantization in future work.The paper also discusses Weyl invariance, realizations on the sphere and punctured plane, and the related, subtle issues on the cylinder, with an eye toward applications to celestial scattering and extended BMS symmetries.

Abstract

The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane. The structure constants are worked out for different choices of bases. The conserved current algebra of non-radiative asymptotically flat spacetimes is explicitly interpreted in these terms.