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**1 - 5**of**5**### Non-planarity through unitarity in ABJM

"... We use unitarity techniques to compute the two-loop non-planar corrections to the Su-dakov form factor and the four-point amplitude in ABJM theory. We start by recon-structing non-planar integrals from two-particle cuts in three dimensions. This causes ambiguities, due to the one-loop four-point amp ..."

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We use unitarity techniques to compute the two-loop non-planar corrections to the Su-dakov form factor and the four-point amplitude in ABJM theory. We start by recon-structing non-planar integrals from two-particle cuts in three dimensions. This causes ambiguities, due to the one-loop four-point amplitude being subleading in dimensional regularization. We provide a prescription to circumvent them and show that it leads to the correct results, as checked against the recent Feynman diagram computation. For the amplitude we point out an alternative basis of integrals, including a non-planar double-box with a numerator inspired by color-kinematics duality. We reproduce the result using a combination thereof with the coefficients fixed by generalized unitarity. For BLG the-ory we propose that this gives the form of the amplitude satisfying color-kinematics duality. Finally, we compute the complete two-loop amplitude of three-dimensional N = 8 SYM, and the corresponding four-point amplitude in N = 16 supergravity as a double copy. 1

### Prepared for submission to JHEP 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 ..."

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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 in-tegrals, we introduce redundancies under certain symmetry considerations to impose the color-kinematics duality of Bern, Carrasco and Johansson (BCJ). For five particles we di-rectly 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 super-gravity 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 rea-son 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. ar X iv