Nonplanarity through unitarity in the ABJM theory

We use unitarity techniques to compute the two-loop nonplanar corrections to the Sudakov form factor and the four-point amplitude in the ABJM theory. We start by reconstructing nonplanar 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 nonplanar 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 the BLG theory, 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. © 2014 American Physical Society.