Scattering Amplitudes/Wilson Loop Duality In ABJM Theory

TL;DR

The paper tests the scattering amplitudes/Wilson loop duality in the 3D ${\cal N}=6$ ABJM theory by computing the planar two-loop four-point amplitude in ${\cal N}=2$ superspace and showing exact agreement with the corresponding light-like Wilson loop. The result exhibits a structure closely mirroring the ${\cal N}=4$ SYM case and supports a BDS-like all-loop ansatz controlled by a three-dimensional scaling function $f_{CS}(\lambda)$ derived from Bethe equations, enabling predictions for higher-loop corrections. The authors discuss dual conformal invariance, proposing that the amplitude can be represented by dual-conformal finite integrals, and they provide a concrete all-loop conjecture along with a four-loop prediction. This work constitutes the first nontrivial evidence of amplitude/WL duality in ABJM and points to deep structural parallels with four-dimensional gauge theories, with avenues for strong-coupling checks and further exploration of dual conformal properties.

Abstract

For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the N=4 SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.

Figures (2)

• Figure 1: Diagrams contributing to the tree level and 1--loop four--point scattering amplitude.
• Figure 2: Diagrams contributing to the two--loop four--point scattering amplitude. The dark--gray blob represents one--loop corrections and the light--gray blob two--loop ones.