Overcoming Obstacles to Colour-Kinematics Duality at Two Loops

Understand

The discovery of colour-kinematics duality has allowed great progress in our understanding of the UV structure of gravity.

• However, it has proven difficult to find numerators which satisfy colour-kinematics duality in certain cases.
• We discuss obstacles to building a set of such numerators in the context of the five-gluon amplitude with all helicities positive at two loops.
• We are able to overcome the obstacles by adding more loop momentum to our numerator to accommodate tension between the values of certain cuts and the symmetries of certain diagrams.