Abstract. The LHC and the advent of gravitational wave observation have motivated tremendous progress in developing approaches to precision predictions in fundamental gauge theories and classical general relativity, and the two can be intimately connected.
The color-kinematics duality of Bern, Carrasco, and Johansson (BCJ) for gauge theories is a duality where, in amplitudes, the kinematic and color weights of graphs obey the same algebraic constraints.
When arranged in such a representation the color-weights can be replaced by another copy of kinematic weights, generating scattering amplitudes for gravitational theories in a procedure known as double-copy construction.
The color-dual form for gauge theory predictions means we only need to fix the physical information in a small number of basis graphs, and algebraic relations propagate this to the full prediction—both at tree-level and importantly at loop-level for the integrand description.