Asymptotic symmetries and subleading soft graviton theorem

TL;DR

This work introduces a generalized BMS group G = ST ⋊ Diff(S^2) that extends asymptotic symmetries of flat spacetime by allowing smooth sphere diffeomorphisms. It develops the radiative phase space framework to define Hamiltonian actions and Ward identities for G, establishing a one-to-one correspondence between these Ward identities and the Cachazo–Strominger subleading soft graviton theorem, while noting the non-closure of the associated algebra. The analysis spans both gravity and a massless scalar field, illustrating intrinsic geometric characterizations and explicit mode-function dynamics, and highlights key challenges in deriving fluxes from first principles due to changes in leading-order data. The results offer a fresh perspective on infrared structure and spacetime symmetries, suggesting pathways to a more complete understanding of soft theorems within a generalized symmetry framework and potential implications for holography and quantum gravity. Overall, the paper provides a concrete link between generalized asymptotic symmetries and the subleading soft graviton sector, while underscoring foundational questions about fluxes and algebra closure that warrant further investigation.

Abstract

Motivated by the equivalence between soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the BMS group, we propose a new extension (different from the so-called extended BMS) of the BMS group which is a semi-direct product of supertranslations and Diff(S^2). We propose a definition for the canonical generators associated to the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.