Soft Graviton Theorem in Arbitrary Dimensions

TL;DR

The paper proves the Cachazo-Strominger soft-graviton conjecture at tree level in arbitrary dimensions by employing the CHY formulation for graviton amplitudes. It performs a careful λ-expansion in the soft momentum, separates the Weinberg leading pole from the subleading term, and demonstrates that the subleading piece equals the action of the total angular momentum operator S^(1) on the (n−1)-point amplitude. The proof relies on two main elements: the orbital angular momentum acting on the scattering-equation deltas and the full angular momentum acting on the determinant E_n, with explicit determinant-derivative and residue calculations. The result extends previous four-dimensional, tree-level soft-gravity results to generic dimensions and highlights the CHY framework's power for universal soft limits, while noting parallel work on the orbital part.

Abstract

In this note we show that the recent conjecture proposed by Cachazo and Strominger holds at tree level in arbitrary dimensions. The proof makes crucial use of the fact that the sub-leading operator is defined using the total angular momentum operator. A key ingredient that makes the proof possible is the CHY formula for graviton amplitudes in arbitrary number of dimensions.