Scattering Amplitudes/Wilson Loop Duality In ABJM Theory

TL;DR

This paper provides evidence for a duality between scattering amplitudes and Wilson loops in ABJM theory, showing their equivalence at two loops and predicting higher-loop corrections based on this duality.

Contribution

It demonstrates the scattering amplitudes/Wilson loop duality in ABJM theory through explicit two-loop calculations and extends the understanding of all-loop amplitude structures.

Findings

Two-loop four-point amplitude matches the Wilson loop result.

Results support a BDS-like ansatz for all-loop amplitudes in ABJM.

Prediction of four-loop correction based on duality and ansatz.

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.