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

Research paper by Johannes Broedel, Lance J. Dixon

Indexed on: 12 Oct '12Published on: 12 Oct '12Published in: Journal of High Energy Physics



Abstract

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 F3, 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 ϕR2 and R3. For operators with higher dimensions than F3, such as F4-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 F4 operators is incompatible with a simple color-kinematics duality based on structure constants fabc, but even the color-compatible F4 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 D2F4 and F5-type operators — does admit the duality, at least for amplitudes with up to six external gluons.