New symmetries for the Gravitational S-matrix

TL;DR

This paper establishes a new symmetry group for asymptotically flat spacetimes in quantum gravity, deriving associated charges from first principles and linking them to known soft graviton theorems.

Contribution

It provides a first principles derivation of Diff(S^2) charges within the generalized BMS group, confirming their connection to soft graviton theorems.

Findings

Diff(S^2) charges are well-defined and derived from first principles.

Leading and subleading soft graviton theorems are equivalent to Ward identities of the new symmetry group.

The generalized BMS group G encompasses symmetries related to soft graviton theorems.

Abstract

In [15] we proposed a generalization of the BMS group G which is a semidirect product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S^2) charges which we could not derive from first principles as G does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S^2) charges. The result of this paper, in conjunction with the results of [4, 15] prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to G.