Note on Soft Graviton theorem by KLT Relation

TL;DR

The note leverages the KLT double-copy framework to derive the soft graviton theorem from the known soft limits of Yang-Mills amplitudes in four dimensions. By selecting a BCJ-compatible KLT form and expanding both YM amplitudes and the momentum kernel, the authors reproduce the leading and subleading gravity soft factors and identify two nontrivial identities of the momentum kernel as necessary consistency conditions. Through explicit n=5 and n=6 examples, they demonstrate how angular-momentum conservation and BCJ relations enforce these identities, though full analytic proofs remain an open challenge. The work suggests a promising route to understanding gravity soft behavior via gauge theory data and motivates further exploration of sub-subleading terms and higher-dimensional generalizations.

Abstract

Recently, new soft graviton theorem proposed by Cachazo and Strominger has inspired a lot of works. In this note, we use the KLT-formula to investigate the theorem. We have shown how the soft behavior of color ordered Yang-Mills amplitudes can be combined with KLT relation to give the soft behavior of gravity amplitudes. As a byproduct, we find two nontrivial identities of the KLT momentum kernel must hold.