Next to subleading soft-graviton theorem in arbitrary dimensions

TL;DR

The paper proves the universality of the next-to-subleading soft-graviton factor in arbitrary dimensions at tree level by employing the CHY formalism. It computes the $M_n^{(2)}$ contribution through a careful, multi-part expansion of delta functions and determinants, capturing all relevant terms. It then applies the $S^{(2)}$ operator to the $(n-1)$-graviton amplitude and shows exact term-by-term agreement with $M_n^{(2)}$, thereby validating the conjectured soft theorem in any dimension. This work reinforces the dimension-independence of the next-to-subleading soft graviton behavior and connects CHY methods with universal gravitational Ward identities at tree level.

Abstract

We study the soft graviton theorem recently proposed by Cachazo and Strominger. We employ the Cachazo, He and Yuan formalism to show that the next to subleading order soft factor for gravity is universal at tree level in arbitrary dimensions.