Evidence for a New Soft Graviton Theorem

TL;DR

The paper investigates a conjectured universal finite subleading soft graviton term and a possible sub-subleading term in the tree-level expansion of graviton scattering amplitudes. Using the spinor-helicity formalism and a holomorphic soft limit together with a BCFW-based factorization, the authors derive and test a universal soft expansion involving $S^{(0)}$, $S^{(1)}$, and $S^{(2)}$ operators. They provide a concrete, all-tree-level proof strategy and verify the resulting relations explicitly for low-point amplitudes (up to six gravitons), including MHV and NMHV configurations, with results matching the Hodges determinant framework. The findings support a deep symmetry-based origin for an infinity of soft relations, potentially tied to a Ward identity for a superrotation Virasoro symmetry, while highlighting caveats related to deformations of hard momenta and quantum corrections.

Abstract

The single-soft-graviton limit of any quantum gravity scattering amplitude is given at leading order by the universal Weinberg pole formula. Gauge invariance of the formula follows from global energy-momentum conservation. In this paper evidence is given for a conjectured universal formula for the finite subleading term in the expansion about the soft limit, whose gauge invariance follows from global angular momentum conservation. The conjecture is non-trivially verified for all tree-level graviton scattering amplitudes using a BCFW recursion relation. One hopes to understand this infinity of new soft relations as a Ward identity for a new superrotation Virasoro symmetry of the quantum gravity S-matrix.