Magnon dispersion to four loops in the ABJM and ABJ models

Understand

The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry which is believed to be integrable in the planar limit.

• However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling.
• We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension.
• We find that all coefficients have maximal transcendentality.