Non-planarity through unitarity in ABJM

Abstract

We use unitarity techniques to compute the two-loop non-planar corrections to the Sudakov form factor and the four-point amplitude in ABJM theory. We start by reconstructing 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 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.

41 pages, 7 figures, misprints corrected, appendix on one-loop d-dimensional cuts added

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Cited by in corpus (13)

• Black holes and the double copy
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Integrated negative geometries in ABJM
• FaRe: a Mathematica package for tensor reduction of Feynman integrals
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Lagrangian Insertion in the Light-Like Limit and the Super-Correlators/Super-Amplitudes Duality
• Unitarity methods for scattering in two dimensions
• A note on scattering amplitudes on the moduli space of ABJM
• The canonical form has got baubles
• On-shell Methods for Form Factors in N=4 SYM and Their Applications