The Duality Between Color and Kinematics and its Applications

2019/09/03 by Zvi Bern, John Joseph M. Carrasco, Bern, Zvi +8 · 140 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Amplitude #Classical mechanics #Computer science #Duality (order theory) #Experimental and Theoretical Physics Studies #Field (mathematics) #Kinematics #Mathematics #Particle Accelerators and Free-Electron Lasers #Physics #Pure mathematics #Quantum mechanics #Scattering amplitude #Theoretical physics #gr-qc #hep-ph #hep-th

paper · pdf · doi:10.48550/arxiv.1909.01358

published in arXiv (Cornell University) (Cornell University) · LaTeX, 37 figures, 208 pages

arxiv created 2019/09/03 · openalex publication_date 2019/09/03 · arxiv updated 2019/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.

Cited by

• Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
• Twisted de Rham theory for string double copy in AdS
• Quasitopological gravity and double-copy formalism
• Magnusian: Relating the Eikonal Phase, the On-Shell Action, and the Scattering Generator
• D-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
• The Double-Copy Root of Hawking Thermality
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Hawking Radiation meets the Double Copy
• Massive Covariant Colour-Kinematics in 3D
• Double copy and the double Poisson bracket
• Superstring amplitudes from the field-theory limit: an n-point map at one loop
• Hidden zeros for higher-derivative YM and GR amplitudes at tree-level
• A homotopy BV algebra for Yang-Mills and color-kinematics
• Relativistic Particle on Light-Front
• Generalized Unitarity Method for Worldline Field Theory
• Limits of Symmetry in Schwarzschild: CKVs and BRST Triviality in the Kerr-Schild Double Copy
• Residual Symmetries and BRST Cohomology of Schwarzschild in the Kerr-Schild Double Copy
• The double copy as a doppelgänger
• Preface to Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Spin versus Magic: Lessons from Gluon and Graviton Scattering
• The Double Copy of Maximal Supersymmetry in D=10
• Gluon amplitudes in first quantization
• Tunnelling amplitudes and Hawking radiation from worldline QFT
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Infrared and Holographic Aspects of the S-Matrix in Gauge Theory and Gravity
• Off-shell double copy theories in BV
• New framework for classical double copies
• Coherent states, background fields, and double copy
• Geometric duality between effective field theories I: scattering amplitudes
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Superstring amplitudes meet surfaceology
• Stringy KLT Relations on AdS
• Double Field Theory as the Double Copy of Yang-Mills
• Tidal Effects in the Post-Minkowskian Expansion
• Exact results for scattering on ultrashort plane wave backgrounds
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Hidden Zeros and 2-split via BCFW Recursion Relation
• From chiral to conformal anomalies: a double copy perspective for CFT correlators
• Carrollian Amplitudes and Holographic Correlators in AdS3/CFT2
• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions

Related

• A Color Dual Form for Gauge-Theory Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 2: An Invitation to Color-Kinematics Duality and the Double Copy
• Colour-Kinematics duality for one-loop rational amplitudes
• Color-Kinematics Duality with Minimal Deformation: Two-Loop Four-Gluon Amplitudes in Pure Yang-Mills Revisited
• Off-shell color-kinematics duality from codifferentials