Plane wave backgrounds and colour-kinematics duality

We consider perturbative gauge theory on a xed Yang-Mills plane wave background, describing its Feynman rules in detail. Using these rules, the tree-level 4-point gluon amplitude is computed. As an application, we investigate whether some notion of colour-kinematics duality | a 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 and highly-constrained structure. This plane wave version
of colour-kinematics duality reduces on a at 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.