Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms

Abstract

Color-kinematics (CK) duality is a remarkable symmetry of gluon amplitudes that is the key to the double copy which links gauge theory and gravity amplitudes. Here we show that the complete Yang-Mills action itself, including its gauge-fixing and ghost sectors required for quantization, can be recast to manifest CK duality using a series of field redefinitions and gauge choices. Crucially, the resulting loop-level integrands are automatically CK-dual, up to potential Jacobian counterterms required for unitarity. While these counterterms may break CK duality, they exist, are unique and, since the tree-level is unaffected, may be deduced from the action or the integrands. Consequently, CK duality is a symmetry of the action like any other symmetry, and it is anomalous in a controlled and mostly harmless sense. Our results apply to any theory with CK-dual tree-level amplitudes. We also show that two CK duality-manifesting parent actions may be factorized and fused into a consistent quantizable offspring, with the double copy as the prime example. This provides a direct proof of the double copy to all loop orders.

arXiv commentv3: 71 pages; arguments, statements, and presentation extended and improved; clarifications added; typos fixed; published version

References in corpus (76)

• 4D Gravity on a Brane in 5D Minkowski Space
• The galileon as a local modification of gravity
• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Leading Quantum Correction to the Newtonian Potential
• Amplitudes, Observables, and Classical Scattering
• Gravity as the Square of Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• Antibracket, Antifields and Gauge-Theory Quantization
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• The classical double copy for Taub-NUT spacetime
• Effective Field Theories from Soft Limits
• Explicit BCJ Numerators from Pure Spinors
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Ambitwistor strings and the scattering equations at one loop
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Universal Field Equations with Covariant Solutions D.B. Fairlie
• Yang-Mills origin of gravitational symmetries
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Classical Physics and Quantum Loops
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Symmetry and Action for Flavor-Kinematics Duality
• BCJ duality and the double copy in the soft limit
• Perturbative Gravity from QCD Amplitudes
• BV Master Action for Heterotic and Type II String Field Theories
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• A Hidden Symmetry of the Galileon
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Amplitude Relations in Non-linear Sigma Model
• Exact solutions for the biadjoint scalar field
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Double Copy from Homotopy Algebras
• A magic pyramid of supergravities
• Euler Hierarchies and Universal Equations
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Are all supergravity theories Yang-Mills squared?
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Double-Copy Constructions and Unitarity Cuts
• Twin Supergravities from Yang-Mills Squared
• Pions as Gluons in Higher Dimensions
• Ehlers as EM duality in the double copy
• On factorizations in perturbative quantum gravity
• A magic square from Yang-Mills squared
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Gravity as the square of Yang-Mills?
• Generalizations of the Double-Copy: the KLT Bootstrap
• The hbar Expansion in Quantum Field Theory
• (2,0) Lagrangian Structures
• $L_{\infty }$-algebras and the perturbiner expansion
• Loop Amplitudes and Quantum Homotopy Algebras
• Superstring loop amplitudes from the field theory limit
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Quantum $L_{\infty }$ Algebras and the Homological Perturbation Lemma
• Linearisation of Universal Field Equations
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• Loop amplitudes monodromy relations and color-kinematics duality
• The single copy of the gravitational holonomy
• The $L_{\infty }$ structure of gauge theories with matter
• Double copy for Lagrangians at trilinear order
• Explicit BCJ numerators of nonlinear sigma model
• Scattering amplitudes in YM and GR as minimal model brackets and their recursive characterization
• Investigation of anomalous axial QED
• Perturbative Quantum Field Theory and Homotopy Algebras
• Odd dimensional analogue of the Euler characteristic

Cited by in corpus (9)

• Kinematic Lie Algebras From Twistor Spaces
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Ambitwistor Yang-Mills Theory Revisited
• Extremal Black Holes from Homotopy Algebras