On the kinematic algebra for BCJ numerators beyond the MHV sector

Abstract

The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain $\mathcal{O}(({\epsilon }_i\cdot {\epsilon }_j{)}^2)$ terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents controls the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.

arXiv comment43 pages, 4 figures

References in corpus (78)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Gravity as the Square of Gauge Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Minimal Basis for Gauge Theory Amplitudes
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• Ambitwistor strings and the scattering equations
• The Momentum Kernel of Gauge and Gravity Theories
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• The Kinematic Algebra From the Self-Dual Sector
• Explicit BCJ Numerators from Pure Spinors
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Conformal Supergravity in Twistor-String Theory
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Ambitwistor strings in 4-dimensions
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Color-Kinematics Duality for QCD Amplitudes
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Algebras for Amplitudes
• Color-kinematic Duality for Form Factors
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Closed String Amplitudes as Single-Valued Open String Amplitudes
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Unifying Relations for Scattering Amplitudes
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Symmetry and Action for Flavor-Kinematics Duality
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• The Kinematic Algebras from the Scattering Equations
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Amplitude Relations in Non-linear Sigma Model
• Berends-Giele recursions and the BCJ duality in superspace and components
• Tree-level Amplitudes in the Nonlinear Sigma Model
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• New Relations for Einstein-Yang-Mills Amplitudes
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• BCJ numerators from reduced Pfaffian
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Heterotic and bosonic string amplitudes via field theory
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Expansion of Einstein-Yang-Mills Amplitude
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• New Identities among Gauge Theory Amplitudes
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Monodromy Relations in Higher-Loop String Amplitudes
• Higher-loop amplitude monodromy relations in string and gauge theory
• Universality in string interactions
• An algebraic approach to BCJ numerators
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Pions as Gluons in Higher Dimensions
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Biadjoint wires
• Unraveling conformal gravity amplitudes
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• Double-Copy Structure of One-Loop Open-String Amplitudes
• String amplitudes from field-theory amplitudes and vice versa
• Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Labelled tree graphs, Feynman diagrams and disk integrals
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
• One-loop monodromy relations on single cuts
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator

Cited by in corpus (37)

• A new gauge-invariant double copy for heavy-mass effective theory
• Double Copy from Homotopy Algebras
• Topology and Wilson lines: global aspects of the double copy
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Covariant Color-Kinematics Duality
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• 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
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• On the Double Copy for Spinning Matter
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Classical Double Copy of Worldline Quantum Field Theory
• Monopoles, shockwaves and the classical double copy
• New heavenly double copies
• Kinematic Lie Algebras From Twistor Spaces
• Classical Spin Gravitational Compton Scattering
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• On the Lagrangian formulation of the double copy to cubic order
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Towards Color-Kinematics Duality in Generic Spacetimes
• Gauge $\times$ Gauge on Spheres
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Kinematic Hopf algebra for amplitudes and form factors
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Flavour-kinematics duality for Goldstone modes
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• BCJ, worldsheet quantum algebra and KZ equations
• A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes
• 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
• The Weyl double copy from twistor space
• Classical gravitational scattering from a gauge-invariant double copy
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories