Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators

We investigate color-kinematics duality for gauge-theory amplitudes produced by the pure nonabelian Yang-Mills action deformed by higher-dimension operators. For the operator denoted by F-3, the product of three field strengths, the existence of color-kinematic dual representations follows from string-theory monodromy relations. We provide explicit dual representations, and show how the double-copy construction of gravity amplitudes based on them is consistent with the Kawai-Lewellen-Tye relations. It leads to the amplitudes produced by Einstein gravity coupled to a dilaton field phi, and deformed by operators of the form phi R-2 and R-3. For operators with higher dimensions than F-3, such as F-4-type operators appearing at the next order in the low-energy expansion of bosonic and superstring theory, the situation is more complex. The color structure of some of the F-4 operators is incompatible with a simple color-kinematics duality based on structure constants f(abc), but even the color-compatible F-4 operators do not admit the duality. In contrast, the next term in the alpha' expansion of the superstring effective action - a particular linear combination of (DF4)-F-2 and F-5 - type operators - does admit the duality, at least for amplitudes with up to six external gluons.