Scattering in ABJ theories

Abstract

We study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using N=2 superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic N>=2 supersymmetric theories and find a vanishing result for N=6 ABJ(M) and N=8 BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Finally we propose a BDS-like exponentiation for the amplitude based on an analogy with the four-dimensional N=4 SYM case, and discuss its strong coupling dual counterpart.

1+54 pages, 8 figures

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• Algebraic structures on parallel M2-branes
• Gluon scattering amplitudes at strong coupling
• Fractional M2-branes
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Cited by in corpus (28)

• Multiple Membranes in M-theory
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
• Unitarity, Crossing Symmetry and Duality in the scattering of $\mathcal{N}=1$ Susy Matter Chern-Simons theories
• One Loop Amplitudes In ABJM
• The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• The 1/2 BPS Wilson loop in ABJM theory at two loops
• An all order identity between ABJM and N=4 SYM four-point amplitudes
• Two-loop effective potentials in general N=2, d=3 chiral superfield model
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Light-like Wilson loops in ABJM and maximal transcendentality
• Two-loop Sudakov Form Factor in ABJM
• Non-planarity through unitarity in ABJM
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• Integrated negative geometries in ABJM
• Self-duality of the D1-D5 near-horizon
• T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)
• ABJM amplitudes and WL at finite N
• FaRe: a Mathematica package for tensor reduction of Feynman integrals
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• On three-point functions in ABJM and the latitude Wilson loop
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• An exact limit of ABJM
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• N=8 SYM vs. N=6 Chern-Simons: Four-point amplitudes at two-loops
• Minimally helicity violating, maximally simple scalar amplitudes in N=4 SYM