Double Soft Graviton Theorems and BMS Symmetries

TL;DR

The paper investigates how double soft graviton theorems, especially consecutive double soft theorems, arise from nested Ward identities of generalized BMS (BMS) symmetries. It shows that leading CDST can be obtained from Ward identities built from two supertranslations and that subleading CDST can be derived from mixed supertranslation–superrotation Ward identities, with the latter involving subtle vacuum structure and contact terms. By mapping these Ward identities to soft-graviton factorization, the work demonstrates that CDSTs correspond to the action of asymptotic symmetries on vacua labeled by soft data, connecting infrared graviton dynamics to BMS charges. The analysis highlights both the power and the subtlety of this symmetry-based approach, including unresolved issues about the precise definition of soft charges and the extension to more general states, while outlining a path toward a deeper understanding of the infrared structure of gravity.

Abstract

It is now well understood that Ward identities associated to the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the sub-leading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated to BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.