Plane wave backgrounds and colour-kinematics duality

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 wellknown identities underpinning the BCJ relations for colour-ordered partial amplitudes, and constrains representations of tree-level amplitudes beyond 4-points.

Classical and quantum double copy of back-reaction

“…While there is still a limited understanding of how double copy applies to observables in general backgrounds, concrete progress has been made for specific backgrounds. It has been shown by studying three-and four-point amplitudes on plane wave backgrounds that a generalization of double copy and colourkinematics duality does persist in the presence of background curvature 1 [25,26].…”

“…Thus, we only need to solve for A µ using the first term on the right-hand-side of (3.14). The required inverse of D 2 is [26]:…”

“…For a spin-2 graviton, the dressed polarization picks up additional background dependence in the form of explicit 'tail' terms. A graviton h µν in the plane wave space-time, subject to gauge conditions n µ h µν = 0 = h µ µ and ∇ µ h µν = 0, can be written 26) where the dressed polarization tensor is not transverse: K µ E µν = 0. This is because K µ E µν = 0 is not equivalent to the covariant gauge-fixing condition ∇ µ h µν in the background.…”

Gluon helicity flip in a plane wave background

“…Propagators for the gluon and quark fields appearing in Yang-Mills and QCD in a plane wave background can be obtained by taking a sum over the linearised states defined above. The Feynman propagator for the gluon in Feynman-'t Hooft gauge was obtained in [15]:…”

The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red

“…Here, the high degree of symmetry frequently allows exact solutions [19][20][21][22], and our results will be exact in the coupling to the background. The same background has been used to test the "double copy" conjecture (for a review see [23]) beyond flat spacetimes [24,25].…”