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

TL;DR

This paper provides a geometric interpretation of color-kinematics duality in gauge and gravity amplitudes, showing how BCJ numerators can be constructed as residues in a moduli space framework, revealing the Jacobi identity as a residue theorem.

Contribution

It introduces a novel geometric perspective on color-kinematics duality, connecting BCJ numerators to intersection numbers and residues in moduli space.

Findings

BCJ numerators obtained as residues around moduli space boundaries

Kinematic Jacobi identity interpreted as a residue theorem

Provides a constructive geometric method for amplitude calculations

Abstract

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.