A Color Dual Form for Gauge-Theory Amplitudes

TL;DR

This work proposes 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.

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.

Figures (4)

• Figure 1: The two diagram types at six points. Each graph can be taken to represent a color factor, a numerator or a set of Feynman propagators.
• Figure 2: An antisymmetric vertex in a cubic graph is replaced by a difference of two double-line vertices.
• Figure 3: Sewing of two vertices in a double-line graph (a). The ordering of the external legs follows the arrow around the graph. This graph corresponds with the kinematic quantity $\tau_{(1342)}$. The same double-line graph is displayed in (b) in a form emphasizing that it is the same quantity whether we sew the two three-point $\tau$'s in the $12$ channel or $13$ channel.
• Figure 4: Cubic diagrams appearing in one-loop four-point amplitudes.