Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes

Abstract

We study 1-loop MHV amplitudes in N=4 super Yang-Mills theory and in N=8 supergravity. For Yang-Mills we find that the simple form for the full amplitude presented by Del Duca, Dixon and Maltoni naturally leads to one that has physical residues on all compact contours. After expanding the simple form in terms of standard scalar integrals, we introduce redundancies under certain symmetry considerations to impose the color-kinematics duality of Bern, Carrasco and Johansson (BCJ). For five particles we directly find the results of Carrasco and Johansson as well as a new compact form for the supergravity amplitude. For six particles we find that all kinematic dual Jacobi identities are encapsulated in a single functional equation relating the expansion coefficients. By the BCJ double-copy construction we obtain a formula for the corresponding N=8 supergravity amplitude. Quite surprisingly, all physical information becomes independent of the expansion coefficients modulo the functional equation. In other words, there is no need to solve the functional equation at all. This is quite welcome as the functional equation we find, using our restricted set of redundancies, actually has no solutions. For this reason we call these results virtual color-kinematics duality. We end with speculations about the meaning of an interesting global vs. local feature of the functional equation and the situation at higher points.

minor changes, version submitted to JHEP

References in corpus (7)

• New Relations for Gauge-Theory Amplitudes
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• BCJ duality and the double copy in the soft limit
• Sharpening The Leading Singularity
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory

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