Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory

Abstract

We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes.

52 pages, 14 figures; v2. a section on loop amplitudes and references added; v3. minor improvements to conform with the published version

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• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
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• Amplitudes of 3d Yang Mills Theory
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
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• Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory
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• All one-loop amplitudes in N=6 superconformal Chern-Simons theory
• Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes
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• ABJM amplitudes and WL at finite N
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• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
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• Fermionic T-duality and U-duality in type II supergravity
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• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• 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
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• ABJM flux-tube and scattering amplitudes
• Deconstructing Supersymmetric S-matrices in D <= 2 + 1
• Yangian Symmetry in Five Dimensions
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Quark-Gluon Plasma: from lattice simulations to experimental results
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• Hidden Local and Non-local Symmetries of S-matrices of N=2,4,8 SYM in D=2+1
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