New symmetries for the Gravitational S-matrix

TL;DR

This paper derives explicit Diff$(S^2)$ charges within a covariant phase space framework by enlarging the radiative phase space to include the conformal sphere metric $q_{AB}$. It shows the induced symplectic structure yields finite charges on an IR-regular subspace and demonstrates that these charges reproduce the Cachazo–Strominger subleading soft graviton theorem as Ward identities for Diff$(S^2)$. The work also provides a Goldstone-mode perspective in which subleading soft gravitons arise from spontaneous breaking of the generalized BMS group to BMS, paralleling the leading soft graviton story. Together, the results cement the role of ${\cal G}$ and Diff$(S^2)$ in the infrared structure of quantum gravity and clarify the phase-space underpinnings of the CS soft theorem.

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.