Double-soft graviton amplitudes and the extended BMS charge algebra

TL;DR

This paper explores how multiple soft graviton scattering amplitudes in 4d Minkowski space encode the BMS charge algebra, revealing an extended structure that persists with quantum corrections and implications for a 2D CFT dual.

Contribution

It demonstrates how double soft graviton amplitudes realize the BMS charge algebra and uncovers an extension that affects the symmetry structure, with potential dual CFT implications.

Findings

The commutator of BMS charges is realized by the antisymmetrized double soft limit.

The extended algebra persists even with quantum corrections.

The extension breaks BMS symmetry if Virasoro superrotations are included.

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.