Relations for Einstein-Yang-Mills amplitudes from the CHY representation

TL;DR

This paper derives relations connecting Einstein-Yang-Mills amplitudes with pure Yang-Mills amplitudes using the CHY representation, generalizing to multiple gravitons and providing a comprehensive formula.

Contribution

It introduces a derivation of Einstein-Yang-Mills amplitude relations from the CHY formalism and generalizes to multiple gravitons with a new formula.

Findings

Derived relations from CHY representation linking Einstein-Yang-Mills and Yang-Mills amplitudes.

Generalized the relations to cases with multiple gravitons.

Provided a universal formula for these generalized amplitude relations.

Abstract

We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and $(n-1)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with $r$ gravitons and $(n-r)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons. We present a general formula for this case.