The Kinematic Algebra From the Self-Dual Sector

Abstract

We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.

29 pages, 5 figures. v2: references added, published version

References in corpus (23)

• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• Gravity, Twistors and the MHV Formalism
• Hyper-K{ä}hler Hierarchies and their twistor theory
• Self-dual Yang--Mills Theory and One-Loop Maximally Helicity Violating Multi-Gluon Amplitudes
• KLT relations from the Einstein-Hilbert Lagrangian
• On factorizations in perturbative quantum gravity
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• Self-Dual Yang-Mills: Symmetries and Moduli Space
• New Relations for Gauge-Theory Amplitudes with Matter
• On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory
• The N=8 Supergravity Hamiltonian as a Quadratic Form
• Monodromy--like Relations for Finite Loop Amplitudes
• Symmetries, Currents and Conservation Laws of Self-Dual Gravity
• The quintic interaction vertex in light-cone gravity
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• On tree amplitudes with gluons coupled to gravitons
• From lightcone actions to maximally supersymmetric amplitudes
• Unusual identities for QCD at tree-level

Cited by in corpus (171)

• Coincident General Relativity
• Black holes and the double copy
• Classical Space-Times from the S Matrix
• Teleparallel Palatini theories
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• 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
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• 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
• The Kerr-Schild double copy in curved spacetime
• Double copy for massive quantum particles with spin
• Algebras for Amplitudes
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Color-kinematic Duality for Form Factors
• One-loop amplitudes on the Riemann sphere
• Gravitational Radiation from Color-Kinematics Duality
• 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
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Symmetry and Action for Flavor-Kinematics Duality
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• BCJ duality and the double copy in the soft limit
• 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
• Gravity as Gauge Theory Squared: A Ghost Story
• Gravity Amplitudes as Generalized Double Copies
• 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
• Amplitude Relations in Non-linear Sigma Model
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• String-inspired BCJ numerators for one-loop MHV amplitudes
• Chiral Higher Spin Theories and Self-Duality
• Kerr-Schild Double Field Theory and Classical Double Copy
• BCJ numerators from reduced Pfaffian
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• S-duality and the Double Copy
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Color/Kinematics Duality in AdS${}_4$
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Expansion of Einstein-Yang-Mills Amplitude
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• A new gauge-invariant double copy for heavy-mass effective theory
• Classical Solutions and their Double Copy in Split Signature
• Double Copy from Homotopy Algebras
• Double Copy for Celestial Amplitudes
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Gluons and gravitons at one loop from ambitwistor strings
• The Classical Double Copy of a Point Charge
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Covariant Color-Kinematics Duality
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Are all supergravity theories Yang-Mills squared?
• 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
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• Twin Supergravities from Yang-Mills Squared
• Pions as Gluons in Higher Dimensions
• 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
• 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
• Classical Double Copy of Worldline Quantum Field Theory
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Strings, extended objects, and the classical double copy
• Self-Dual Gravity
• Unraveling conformal gravity amplitudes
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Celestial holography on Kerr-Schild backgrounds
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• New heavenly double copies
• Kinematic Lie Algebras From Twistor Spaces
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Asymptotic Weyl Double Copy
• Classical Spin Gravitational Compton Scattering
• Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Algorithmic construction of SYM multiparticle superfields in the BCJ gauge
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• MHV scattering of gluons and gravitons in chiral strong fields
• 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
• Amplitudes, Hopf algebras and the colour-kinematics duality
• On the Lagrangian formulation of the double copy to cubic order
• The double copy of the multipole expansion
• Towards Color-Kinematics Duality in Generic Spacetimes
• Virtuous Trees at Five and Six Points for Yang-Mills and Gravity
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Non-perturbative aspects of the self-dual double copy
• Gauge $\times$ Gauge on Spheres
• Geodesics From Classical Double Copy
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Off-shell Currents and Color-Kinematics Duality
• One-loop monodromy relations on single cuts
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• On-Shell Covariance of Quantum Field Theory Amplitudes
• Dual-color decompositions at one-loop level in Yang-Mills theory
• The single copy of the gravitational holonomy
• Flat Self-dual Gravity
• More on the Classical Double Copy in Three Spacetime Dimensions
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• The Complete KLT-Map Between Gravity and Gauge Theories
• Kinematic Hopf algebra for amplitudes and form factors
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Non-perturbative Double Copy in Flatland
• On Primary Relations at Tree-level in String Theory and Field Theory
• 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
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• The double copy: gravity from gluons
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Double copy for Lagrangians at trilinear order
• Note on symmetric BCJ numerator
• The Construction of Dual-trace Factor in Yang-Mills Theory
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
• Effective observables for electromagnetic duality from novel amplitude decomposition
• One-loop SYM-supergravity relation for five-point amplitudes
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Color kinematic symmetric (BCJ) numerators in a light-like gauge
• Quantum gates via relativistic remote control
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Flavour-kinematics duality for Goldstone modes
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• The double copy: from optics to quantum gravity
• Entanglement and the Double Copy
• Constraining higher-spin S-matrices
• BCJ, worldsheet quantum algebra and KZ equations
• Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians
• BCJ Numerators from Differential Operator of Multidimensional Residue
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
• Double copy for tree-level form factors. Part II. Generalizations and special topics
• Next-to-MHV Yang-Mills kinematic algebra
• A new Wilson line-based action for gluodynamics
• One-Loop Effective Action Approach to Quantum MHV Theory
• Hawking radiation from the double copy
• Self-dual gravity via Hitchin's equations
• Notes on self-dual gravity
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Gravity model from (A)dS Yang-Mills theory
• Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes
• On self-dual Yang-Mills fields on special complex surfaces
• Tree-level scattering amplitudes in nonlocal field theories
• Geometric duality between effective field theories I: scattering amplitudes