Manifesting Color-Kinematics Duality in the Scattering Equation Formalism

TL;DR

This paper demonstrates how the scattering equation formalism for Yang-Mills amplitudes can explicitly reveal the color-kinematics duality through a specific reduction algorithm, building on recent amplitude identities.

Contribution

It introduces a concrete reduction algorithm that makes the color-kinematics duality manifest term-by-term in the scattering equation formalism.

Findings

The reduction algorithm explicitly demonstrates the duality.

Generalizes identities between gravity and Yang-Mills amplitudes.

Connects scattering equations with monodromy relations in string theory.

Abstract

We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory's color-kinematics duality. This is achieved through a concrete reduction algorithm which renders this duality manifest term-by-term. The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory. A byproduct of our algorithm is a generalization of the identities among gravity and Yang-Mills amplitudes.