Scattering in ABJ theories

TL;DR

This paper investigates the duality between scattering amplitudes and Wilson loops in three-dimensional supersymmetric Chern-Simons theories, revealing conditions for duality validity and proposing a BDS-like exponentiation for amplitudes.

Contribution

It computes one- and two-loop four-point superamplitudes in N≥2 theories, finds vanishing results for certain models, and extends Wilson loop/amplitude duality analysis to ABJ theories with a proposed exponentiation.

Findings

One-loop superamplitudes vanish for N=6 ABJ(M) and N=8 BLG models.

Two-loop ABJ amplitude matches Wilson loop results, confirming duality in certain cases.

Dual conformal invariance holds up to a residual constant 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.