Double-soft graviton amplitudes and the extended BMS charge algebra

TL;DR

This work demonstrates that the BMS charge algebra in four-dimensional Minkowski space is realized in scattering amplitudes through antisymmetrized consecutive double-soft graviton limits. The analysis identifies an extension term K that modifies the algebra when local superrotations are included, while the hard sector remains governed by the standard commutator structure. The extension obeys a generalized cocycle condition, preserving Jacobi consistency and signaling a Lie algebroid-like structure rather than a pure Lie algebra. The paper also outlines a 2d algebraic picture on the celestial sphere, suggesting avenues toward a possible flat-space holographic description, while acknowledging unresolved questions about central charges and the precise 2d dual. Overall, the results reinforce the stability of BMS symmetries in quantum gravity contexts and illuminate how soft theorems encode asymptotic symmetry data in the S-matrix framework.

Abstract

We discuss how scattering amplitudes in 4d Minkowski spacetime which involve multiple soft gravitons realize the algebra of BMS charges on the null boundary. In particular, we show how the commutator of two such charges is realized by the antisymmetrized consecutive soft limit of the double soft amplitude. The commutator is found to be robust even in the presence of quantum corrections, and the associated Lie algebra has an extension, which breaks the BMS symmetry if the BMS algebra is taken to include the Virasoro algebra of local superrotations. We discuss the implications of this structure for the existence of a 2d CFT dual description for 4d scattering amplitudes.