Plane wave backgrounds and colour-kinematics duality

TL;DR

This paper derives Feynman rules for gauge theory on a plane wave background, computes gluon amplitudes, and investigates the validity of colour-kinematics duality in this setting, revealing constrained obstructions.

Contribution

It provides the first detailed Feynman rules for perturbative gauge theory on a plane wave background and analyzes the modified colour-kinematics duality in this context.

Findings

Colour-kinematics duality is obstructed on the plane wave background.

The obstruction has a constrained structure.

The duality reduces to BCJ identities in flat space.

Abstract

We obtain the detailed Feynman rules for perturbative gauge theory on a fixed Yang-Mills plane wave background. Using these rules, the tree-level 4-point gluon amplitude is computed and some 1-loop Feynman diagrams are considered. As an application, we test the extent to which colour-kinematics duality, the relation between the colour and kinematic constituents of the amplitude, holds on the plane wave background. Although the duality is obstructed, the obstruction has an interesting constrained structure. This plane wave version of colour-kinematics duality reduces on a flat background to the well-known identities underpinning the BCJ relations for colour-ordered partial amplitudes, and constrains representations of tree-level amplitudes beyond 4-points.