Generalized BMS charge algebra

TL;DR

The paper extends the gravitational phase space at null infinity to include Diff(S^2) and builds a canonical realization of the generalized BMS (GBMS) algebra. By introducing a ψ-potential and a Diff(S^2)-covariant derivative, it covariantizes non-Bondi frame data and defines a corrected super angular momentum J_V whose Poisson brackets with supertranslations reproduce the GBMS structure without unwanted extension terms. A split of charges into hard, soft, and boundary contributions, together with a carefully constructed symplectic form Ω = Ω^I + Ω^S^2 on an extended phase space Γ, yields the desired PBs: {P_f, P_f'}=0, {J_V, P_f}=P_{V(f)}, and {J_V, J_{V'}}=J_{[V,V']}. The framework unifies Bondi and non-Bondi frames, preserves S-matrix Ward identities, and highlights a path toward realizing GBMS symmetries in the gravitational S-matrix, while outlining open questions about covariant-phase-space derivations and higher-dimensional generalizations.

Abstract

It has been argued that the symmetries of gravity at null infinity should include a Diff$(S^2)$ factor associated to diffeomorphisms on the celestial sphere. However, the standard phase space of gravity does not support the action of such transformations. Building on earlier work by Laddha and one of the authors, we present an extension of the phase space of gravity at null infinity on which Diff$(S^2)$ acts canonically. The Poisson brackets of supertranslation and Diff$(S^2)$ charges reproduce the generalized BMS algebra introduced in arXiv:1408.2228 .