A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator

Abstract

We derive a vertex operator based expression for the kinematic numerators of Yang-Mills amplitudes by applying the momentum kernel formalism to open string amplitudes. The expression involves an ${\alpha }^{\prime }$-weighted commutator induced by the monodromy relations between the colour ordered Yang-Mills amplitudes, which mirrors the ${\alpha }^{\prime }$ deformed colour structure observed in open string and semi-abelian $Z$-theory. The kinematic algebra given by this construction contains the Lie algebra of diffeomorphism as an obvious sub-algebra.

arXiv comment25 pages. v2: minor corrections version to be published

References in corpus (60)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Gravity as the Square of Gauge Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Black holes and the double copy
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• The classical double copy for Taub-NUT spacetime
• Explicit BCJ Numerators from Pure Spinors
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Algebras for Amplitudes
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Scattering on plane waves and the double copy
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Spinning particles, axion radiation, and the classical double copy
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• 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
• Proof of Gravity and Yang-Mills Amplitude Relations
• Berends-Giele recursion for double-color-ordered amplitudes
• Amplitude Relations in Non-linear Sigma Model
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• BCJ numerators from reduced Pfaffian
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Are all supergravity theories Yang-Mills squared?
• An algebraic approach to BCJ numerators
• A Color Dual Form for Gauge-Theory Amplitudes
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• Twin Supergravities from Yang-Mills Squared
• BCJ duality and double copy in the closed string sector
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• On Primary Relations at Tree-level in String Theory and Field Theory
• Note on New KLT relations
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Consistent Off-Shell Tree String Amplitudes

Cited by in corpus (13)

• A new gauge-invariant double copy for heavy-mass effective theory
• Covariant Color-Kinematics Duality
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Loop amplitudes monodromy relations and color-kinematics duality
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• BCJ, worldsheet quantum algebra and KZ equations
• Next-to-MHV Yang-Mills kinematic algebra
• Building Momentum Kernel from Shapovalov Form