Colour-Kinematics Duality for One-Loop Rational Amplitudes

Abstract

Colour-kinematics duality is the conjecture of a group theory-like structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar progress has been lacking at loop level, where the power of the duality would be most significant. Here we explore colour-kinematics duality at one loop using the self-dual sector as a starting point. The duality is shown to exist in pure Yang-Mills theory for two infinite classes of amplitudes: amplitudes with any number of particles either all of the same helicity or with one particle helicity opposite the rest. We provide a simple Lagrangian-based argument in favour of the double copy relation between gauge theory and gravity amplitudes in these classes, and provide some explicit examples. We further discuss aspects of the duality which persist after integration, leading to relations among partial amplitudes. Finally, we describe form factors in the self-dual theory at tree level which also satisfy the duality.

36 pages, 5 figures; v2: published version

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• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
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• One-loop amplitudes on the Riemann sphere
• Color-kinematic Duality for Form Factors
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
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• The self-dual classical double copy, and the Eguchi-Hanson instanton
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• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
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• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Gluons and gravitons at one loop from ambitwistor strings
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Double-Copy Constructions and Unitarity Cuts
• A double copy for asymptotic symmetries in the self-dual sector
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Twin Supergravities from Yang-Mills Squared
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Weyl doubling
• The Newman-Penrose Map and the Classical Double Copy
• BCJ duality and double copy in the closed string sector
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Celestial chiral algebras, colour-kinematics duality and integrability
• Monopoles, shockwaves and the classical double copy
• Gauge and Gravity Amplitude Relations
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• Unraveling conformal gravity amplitudes
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
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• Kinematic Lie Algebras From Twistor Spaces
• On loop celestial amplitudes for gauge theory and gravity
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Conformal Gravity from Gauge Theory
• Twistor Space Origins of the Newman-Penrose Map
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
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• Gauge $\times$ Gauge on Spheres
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• Dual-color decompositions at one-loop level in Yang-Mills theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• Full-color three-loop three-point form factors in N=4 SYM
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Kinematic Hopf algebra for amplitudes and form factors
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• Note on symmetric BCJ numerator
• The Construction of Dual-trace Factor in Yang-Mills Theory
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
• Explicit BCJ numerators of nonlinear sigma model
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Color kinematic symmetric (BCJ) numerators in a light-like gauge
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• BCJ, worldsheet quantum algebra and KZ equations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
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• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Note on off-shell relations in nonlinear sigma model
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• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• Scalar Gravity and the Double Copy in the Framework of General Relativity
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations