Sub-sub-leading soft-graviton theorem in arbitrary dimension

TL;DR

This paper proves the sub-sub-leading soft-graviton theorem for tree-level amplitudes in arbitrary dimensions by a direct calculation using the CHY representation. It performs a meticulous higher-point expansion around the soft graviton and simultaneously constructs the same result from the lower-point amplitude via the proposed S^{(2)} soft factor, which involves orbital and spin angular momentum actions. The two computational routes are shown to coincide, establishing the universality of the sub-sub-leading term in any dimension and extending prior four-dimensional results. Detailed residue analyses are provided in Appendices to support the equivalence between the two approaches.

Abstract

The CHY formula which describes an $n$-point tree level scattering amplitude for scalars, gluons or gravitons in arbitrary dimension [22], is used to prove the sub-sub-leading soft- graviton theorem recently proposed by Cachazo and Strominger [13].