BMS supertranslations and Weinberg's soft graviton theorem

TL;DR

Strominger et al. show that Weinberg's soft graviton theorem is equivalent to the Ward identity of a diagonal BMS supertranslation symmetry acting across ${\mathscr I}^-$ and ${\mathscr I}^+$. They build the physical radiative phase spaces including soft boundary modes, and derive a modified Dirac bracket that yields canonical generators $T^\pm(f)$, ensuring proper action of supertranslations on infrared data. They interpret soft gravitons as Goldstone modes of spontaneously broken supertranslation invariance and provide the mapping between asymptotic data and momentum-space soft factors, thereby unifying the infrared graviton physics with asymptotic symmetries. The work also lays groundwork for extending these insights to gauge theories and clarifies the role of boundary conditions in implementing the symmetry on the S-matrix.

Abstract

Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity (${\mathscr I}^-$ and ${\mathscr I}^+$) is an exact symmetry of the quantum gravity ${\cal S}$-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg's soft graviton theorem. Along the way we construct the canonical generators of supertranslations at ${\mathscr I}^\pm$, including the relevant soft graviton contributions. Boundary conditions at the past and future of ${\mathscr I}^\pm$ and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.