Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory

Abstract

In this paper we study the one- and two-loop corrections to the four-point amplitude of N=6 Chern-Simons matter theory. Using generalized unitarity methods we express the one- and two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the two-loop result is non-vanishing and matches with the Wilson loop computation. Furthermore, the two-loop correction takes the same form as the one-loop correction to the four-point amplitude of N=4 super Yang-Mills. We discuss possible higher loop extensions of this correspondence between the two theories. As a side result, we extend the method of dimensional reduction for three dimensions to five dimensions where dual conformal symmetry is most manifest, demonstrating significant simplification to the computation of integrals.

32 pages and 6 figures. v2: minus sign corrections, ref updated v3: Published version

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• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• Non-planarity through unitarity in ABJM
• All one-loop amplitudes in N=6 superconformal Chern-Simons theory
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
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• T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)
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• FaRe: a Mathematica package for tensor reduction of Feynman integrals
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• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• The two-loop eight-point amplitude in ABJM theory
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• An exact limit of ABJM
• N=8 SYM vs. N=6 Chern-Simons: Four-point amplitudes at two-loops
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• ABJM flux-tube and scattering amplitudes
• Yangian Symmetry in Five Dimensions
• $\mathcal{N}=3$ Harmonic Super-Wilson Loop
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle