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Manifesting Color-Kinematics Duality in the Scattering Equation Formalism

N. E. J. Bjerrum-Bohr, Jacob L. Bourjaily, Poul H. Damgaard, Bo Feng

TL;DR

<3-5 sentence high-level summary>

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.

Manifesting Color-Kinematics Duality in the Scattering Equation Formalism

TL;DR

<3-5 sentence high-level summary>

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.

Paper Structure

This paper contains 9 sections, 42 equations.

Table of Contents

  1. Introduction
  2. Review: Amplitudes in the Scattering Equation Formalism
  3. Color-Kinematics Duality in the CHY Representation
  4. The Algorithm: Manifesting the Color-Kinematics Duality
  5. Fundamental Operations, Identities, and Diagrammatic Notation
  6. The Systematic Reduction of Terms
  7. Proof of Recursive Reduction to Single Cycles
  8. Application: the Four-Particle Amplitude in Yang-Mills
  9. Conclusions