Magnon dispersion to four loops in the ABJM and ABJ models

TL;DR

This paper calculates the four-loop magnon dispersion function in ABJM and ABJ models using perturbation theory, confirming predictions from the Y-system and exploring potential all-loop integrability.

Contribution

It provides the explicit four-loop computation of the magnon dispersion function and wrapping correction, extending understanding of integrability in these models.

Findings

Coefficients exhibit maximal transcendentality.

Four-loop wrapping correction matches Y-system predictions.

Proposes a limit of ABJ model with potential all-loop integrability.

Abstract

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. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.