Tree-level color–kinematics duality implies loop-level color–kinematics duality up to counterterms

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