Note on Identities Inspired by New Soft Theorems

TL;DR

This paper explores new amplitude identities inspired by soft theorems in gravity and gauge theories, proving them using the CHY formulation and discussing their implications for amplitude relations.

Contribution

It introduces and proves two sets of amplitude identities related to soft theorems, including identities involving the half-soft function and the KLT momentum kernel.

Findings

Proved an identity involving the half-soft function using CHY formulation.

Derived identities involving the KLT momentum kernel as consistency conditions.

Enhanced understanding of amplitude relations inspired by soft theorems.

Abstract

The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set includes an identity involving the half-soft function which had been used in the soft theorem for one-loop rational gravity amplitudes, and another simpler identity as its byproduct. The second set includes two identities involving the KLT momentum kernel, as the consistency conditions of the KLT relation plus soft theorems for both gravity and gauge amplitudes. We use the CHY formulation to prove the first identity, and transform the second one into a convenient form for future discussion.