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

Abstract

A bstract 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 ϕ , and deformed by operators of the form ϕR 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 α ′ expansion of the superstring effective action — a particular linear combination of D 2 F 4 and F 5 -type operators — does admit the duality, at least for amplitudes with up to six external gluons.