Plane wave backgrounds and colour-kinematics duality

TL;DR

This work develops perturbative Yang–Mills theory on a nontrivial plane-wave background, deriving complete Feynman rules and computing tree-level 3- and 4-point gluon amplitudes. It then tests colour-kinematics duality in this curved setting, finding an obstruction governed by background-induced tensor structures that nevertheless preserves a constrained, calculable form that reduces to flat-space CK relations in the appropriate limit. The results provide a concrete data set for exploring plane-wave double copy to gravity and set the stage for higher-point, loop, and ambitwistor-string investigations on curved backgrounds. Overall, the paper demonstrates that CK duality persists in a structured way on plane-wave backgrounds and offers several clear directions for extending CK/dual-copy ideas beyond flat spacetime.

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.

Figures (4)

• Figure 1: The sandwich plane wave with $x^a$-directions suppressed. The field strength $F_{a}=\dot{A}_{a}(x^-)$ is non-zero only in the shaded region; the gauge field is flat on the in- and out-regions.
• Figure 2: The three- and four-point gluon vertices
• Figure 3: The ghost vertex
• Figure 4: The ghost loop contribution to the gluon self-energy