Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes

Understand

We give a geometric interpretation of color-kinematics duality between tree-level scattering amplitudes of gauge and gravity theories.

• Using their representation as intersection numbers we show how to obtain Bern-Carrasco-Johansson numerators in a constructive way as residues around boundaries of the moduli space.
• In this language the kinematic Jacobi identity between each triple of numerators is a residue theorem in disguise.