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.

v3: 71 pages; arguments, statements, and presentation extended and improved; clarifications added; typos fixed; published version

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Cited by in corpus (9)

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• 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