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. (c) 2023 The Author(s).
Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
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