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

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.

5 pages, title change to match the published version

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Cited by in corpus (39)

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• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
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• Baikov representations, intersection theory, and canonical Feynman integrals
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• Celestial double copy from the worldsheet
• New heavenly double copies
• Kinematic Lie Algebras From Twistor Spaces
• Cosmology meets cohomology
• Classical Spin Gravitational Compton Scattering
• Amplitudes, Hopf algebras and the colour-kinematics duality
• On the Lagrangian formulation of the double copy to cubic order
• Superstring loop amplitudes from the field theory limit
• Towards Color-Kinematics Duality in Generic Spacetimes
• Geodesics From Classical Double Copy
• Loop amplitudes monodromy relations and color-kinematics duality
• Kinematic Hopf algebra for amplitudes and form factors
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• A Lie bracket for the momentum kernel
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Correlation functions on the lattice and twisted cocycles
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Ambitwistor Integrands from Tensionless Chiral Superstring Integrands
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• On Chiral Splitting and the Ambitwistor String
• The Holographic Soft $S$-Matrix in QED and Gravity
• Seiberg-Witten map Invariant Scatterings
• One-loop diagrams with quadratic propagators from the worldsheet
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
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• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• Next-to-MHV Yang-Mills kinematic algebra
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• Holographic Representations of Supertranslation Eigenstates