Algebras for Amplitudes

Abstract

Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in gauge theory amplitudes. The basis is constructed making use of the KK and BCJ relations, thereby showing precisely how these relations underlie the color-kinematics duality. We express gravity amplitudes in terms of a related basis of color-dressed gauge theory amplitudes, with basis coefficients which are permutation symmetric.

17 pages, 1 figure. v2: published version, example added in appendix

References in corpus (20)

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• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
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• New Relations for Gauge-Theory Amplitudes with Matter
• New relations for scattering amplitudes in Yang-Mills theory at loop level
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Cited by in corpus (103)

• Black holes and the double copy
• Classical Space-Times from the S Matrix
• 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
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Scattering Amplitudes from Intersection Theory
• The Kerr-Schild double copy in curved spacetime
• Double copy for massive quantum particles with spin
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Color-kinematic Duality for Form Factors
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Type D Spacetimes and the Weyl Double Copy
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Gravity as Gauge Theory Squared: A Ghost Story
• The Kinematic Algebras from the Scattering Equations
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
• Amplitude Relations in Non-linear Sigma Model
• String-inspired BCJ numerators for one-loop MHV amplitudes
• Exact solutions for the biadjoint scalar field
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• S-duality and the Double Copy
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Expansion of Einstein-Yang-Mills Amplitude
• A new gauge-invariant double copy for heavy-mass effective theory
• Double Copy from Homotopy Algebras
• 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
• Covariant Color-Kinematics Duality
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Scattering Equations and Feynman Diagrams
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Extended solutions for the biadjoint scalar field
• An algebraic approach to BCJ numerators
• 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
• Are all supergravity theories Yang-Mills squared?
• Twin Supergravities from Yang-Mills Squared
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• The Newman-Penrose Map and the Classical Double Copy
• Weyl doubling
• On the Double Copy for Spinning Matter
• Strings, extended objects, and the classical double copy
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Inverse of the String Theory KLT Kernel
• New heavenly double copies
• Kinematic Lie Algebras From Twistor Spaces
• UV considerations on scattering amplitudes in a web of theories
• Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• Twistor Space Origins of the Newman-Penrose Map
• $L_{\infty }$-algebras and the perturbiner expansion
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• On the Lagrangian formulation of the double copy to cubic order
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Geodesics From Classical Double Copy
• Gauge $\times$ Gauge on Spheres
• Off-shell Currents and Color-Kinematics Duality
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• Dual-color decompositions at one-loop level in Yang-Mills theory
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• The Complete KLT-Map Between Gravity and Gauge Theories
• Non-perturbative Double Copy in Flatland
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Unified web for expansions of amplitudes
• The Infrared Structure of Exceptional Scalar Theories
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• The Construction of Dual-trace Factor in Yang-Mills Theory
• Note on symmetric BCJ numerator
• Explicit BCJ numerators of nonlinear sigma model
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
• Effective observables for electromagnetic duality from novel amplitude decomposition
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Color structures and permutations
• Factorization of cubic vertices involving three different higher spin fields
• Generalized Yang-Mills Theory and Gravity
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• A String Deformation of the Parke-Taylor Factor
• Double Copy of Form Factors and Higgs Amplitudes: A mechanism of turning spurious poles in Yang-Mills into physical poles in gravity
• BCJ, worldsheet quantum algebra and KZ equations
• Double copy for tree-level form factors. Part I. Foundations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Double copy for tree-level form factors. Part II. Generalizations and special topics
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Next-to-MHV Yang-Mills kinematic algebra
• Note on off-shell relations in nonlinear sigma model
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
• The seeds of EFT double copy