The Bethe ansatz for superconformal Chern-Simons

Abstract

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin chain with sites alternating between the fundamental and the anti-fundamental representations. We find a set of Bethe equations from which the anomalous dimensions can be determined and give a proposal for the Bethe equations to the full superconformal group of OSp(2,2|6).

22 pages, 9 figures; v2 Overall normalization of the Hamiltonian corrected and missing diagram contributing to two-site interactions included. Typos fixed; v3 Figure 8 corrected; v4 Misprints corrected; v5 Correct figures recovered. Published version; v6: misprints in (3.15), (3.16), (3.17) corrected

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• Boundary bound states and integrable Wilson loops in ABJM
• Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain