Center-less BMS charge algebra

TL;DR

This work shows that enforcing Wald–Zoupas covariance yields a centerless current algebra for BMS and removes the frame-dependent 2-cocycle from the charge algebra on arbitrary cuts, by incorporating a covariant symplectic potential and a refined treatment of boundary data. It introduces a Goldstone-improved covariant super-momentum and a covariant, corner-term–based extension that also handles the extended BMS symmetry (eBMS), though a time-independent cocycle tied to edge data persists in the full eBMS charge algebra. The analysis hinges on Geroch’s tensor and an anomaly operator that tracks background dependence under conformal and foliation changes, providing a practical framework to diagnose covariance losses and ambiguities in radiative spacetimes. Overall, the results sharpen the understanding of boundary symmetries in general relativity and offer covariant prescriptions to resolve ambiguities in radiative charge constructions, with implications for celestial holography and IR gravitational physics.

Abstract

We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for application to the charge aspects, and introduce a new aspect for Geroch's super-momentum with better covariance properties. For the extended BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas symplectic potential exists, if one is willing to modify the symplectic structure by a corner term. The resulting algebra of Noether currents between two arbitrary cuts is center-less. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and non-radiative. More precisely, super-rotation fluxes act covariantly, but super-rotation charges act covariantly only on global translations. The take home message is that in any situation where 2-cocycles appears in the literature, covariance has likely been lost in the charge prescription, and that the criterium of covariance is a powerful one to reduce ambiguities in the charges, and can be used also for ambiguities in the charge aspects.