A Color Dual Form for Gauge-Theory Amplitudes

TL;DR

This paper introduces a new representation of gauge-theory amplitudes that swaps the roles of color and kinematics, revealing a deeper duality and potential extensions to loop calculations.

Contribution

It proposes a novel dual form of gauge-theory amplitudes that reorganizes the structure by interchanging color and kinematic factors, extending the color decomposition framework.

Findings

Revealed a deeper color-kinematics duality in gauge theories.

Established a reversible relationship between different amplitude forms.

Discussed potential extensions to loop-level amplitudes.

Abstract

Recently a duality between color and kinematics has been proposed, exposing a new unexpected structure in gauge theory and gravity scattering amplitudes. Here we propose that the relation goes deeper, allowing us to reorganize amplitudes into a form reminiscent of the standard color decomposition in terms of traces over generators, but with the role of color and kinematics swapped. By imposing additional conditions similar to Kleiss-Kuijf relations between partial amplitudes, the relationship between the earlier form satisfying the duality and the current one is invertible. We comment on extensions to loop level.