Sub-subleading soft gravitons and large diffeomorphisms

TL;DR

This paper demonstrates that the sub-subleading soft graviton theorem at tree level corresponds to Ward identities of a new class of asymptotic vector fields beyond the established generalized BMS algebra, using a de Donder-gauge covariant phase space framework. It derives finite charges for these symmetries, showing that their hard and soft parts reproduce the sub-subleading structure and connects CK constraints to magnetic Weyl charges. An electric/magnetic Weyl-tensor interpretation is developed, arguing that the magnetic charges encode the missing helicity content and CK-type constraints, while the electric charges recover known generalized BMS charges. The work also outlines unresolved issues around symmetry closure, the interpretation of these large diffeomorphisms, and the fate of these charges when loop corrections are included.

Abstract

We present strong evidence that the sub-subleading soft theorem in semi-classical (tree level) gravity discovered by Cachazo and Strominger is equivalent to the conservation of asymptotic charges associated to a new class of vector fields not contained within the previous extensions of BMS algebra. Our analysis crucially relies on analyzing the hitherto established equivalences between soft theorems and Ward identities from a new perspective. In this process we naturally (re)discover a class of `magnetic' charges at null infinity that are associated to the dual of the Weyl tensor.