Magnon dispersion to four loops in the ABJM and ABJ models

Details Magnon dispersion to four loops in the ABJM and ABJ models Magnon dispersion to four loops in the ABJM and ABJ models

2009-08-17

arxiv.org/abs/0908.2463v3

J.Phys.A43:275402,2010

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram corrected: modified result in the ABJ case only, formulati

Scientific paper

10.1088/1751-8113/43/27/275402

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.

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