Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

Abstract

We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.

35 page, 10 figures, REVTex, ancillary mathematica file containing one-loop diagram numerators, latest version includes updated references, corrected two-loop numerators and various clarifications

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• New Relations for Gauge-Theory Amplitudes
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• Color-kinematic Duality for Form Factors
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• BCJ duality and the double copy in the soft limit
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• Gravity from Rational Curves
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
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Cited by in corpus (107)

• Black holes and the double copy
• The classical double copy for Taub-NUT spacetime
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Double copy for massive quantum particles with spin
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Gravity Amplitudes as Generalized Double Copies
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Exact solutions for the biadjoint scalar field
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• S-duality and the Double Copy
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• A new gauge-invariant double copy for heavy-mass effective theory
• Double Copy from Homotopy Algebras
• Graviton-Photon Scattering
• Topology and Wilson lines: global aspects of the double copy
• 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
• Higher-loop amplitude monodromy relations in string and gauge theory
• Double-Copy Constructions and Unitarity Cuts
• Are all supergravity theories Yang-Mills squared?
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Twin Supergravities from Yang-Mills Squared
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Gravitational radiation from the classical spinning double copy
• Two-Loop Renormalization of Quantum Gravity Simplified
• Weyl doubling
• Sources in the Weyl double copy
• BCJ duality and double copy in the closed string sector
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Monopoles, shockwaves and the classical double copy
• Plane wave backgrounds and colour-kinematics duality
• Biadjoint wires
• Self-Dual Gravity
• Unraveling conformal gravity amplitudes
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Double copy structure of parity-violating CFT correlators
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• One-loop Correlators and BCJ Numerators from Forward Limits
• Einstein-Maxwell theory and the Weyl double copy
• Twistor Space Origins of the Newman-Penrose Map
• Conformal Gravity from Gauge Theory
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• On the Lagrangian formulation of the double copy to cubic order
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Gauge $\times$ Gauge on Spheres
• Off-shell Currents and Color-Kinematics Duality
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Dual-color decompositions at one-loop level in Yang-Mills theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Full-color three-loop three-point form factors in N=4 SYM
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Kinematic Hopf algebra for amplitudes and form factors
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Beyond the standard model with six-dimensional spinors
• One-Loop Yang-Mills Integrands from Scattering Equations
• Explicit BCJ numerators of nonlinear sigma model
• Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order
• Regularized Weyl double copy
• The Mile High Magic Pyramid
• Generalized Yang-Mills Theory and Gravity
• The Magic Star of Exceptional Periodicity
• Symmetrization of Jordan dialgebras
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Flavour-kinematics duality for Goldstone modes
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Loop-level double-copy for massive fermions in the fundamental
• BCJ, worldsheet quantum algebra and KZ equations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
• Non-Abelian gauged supergravities as double copies
• Off-shell BCJ Relation in Nonlinear Sigma Model
• Next-to-MHV Yang-Mills kinematic algebra
• Note on off-shell relations in nonlinear sigma model
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• From U(1) to E8: soft theorems in supergravity amplitudes
• The Weyl double copy from twistor space
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Scattering amplitudes in gauge theories with and without supersymmetry
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Color-factor symmetry and BCJ relations for QCD amplitudes
• Weyl double copy in Lifshitz spacetimes