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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• Three-dimensional N=6 SCFT's and their membrane dynamics
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• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• The AdS4/CFT3 algebraic curve
• Anomalous radius shift in AdS(4)/CFT(3)
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Comment on the Scaling Function in AdS4 x CP3
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Non-planar ABJM Theory and Integrability
• Non-planar ABJ Theory and Parity
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• A note on the reduction of the AdS4 x CP3 string sigma model
• Giant Magnons on CP^3 by Dressing Method
• Dressed Giant Magnons on CP^3
• Observables and Correlators in Nonrelativistic ABJM Theory
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Factorized Tree-level Scattering in AdS_4 x CP^3
• The Morphology of N=6 Chern-Simons Theory
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Zero Modes for the Boundary Giant Magnons
• Semiclassical strings in AdS(3) X S^2
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• Dilatation operator in 3d
• Fermionic reductions of the AdS4 x CP3 superstring
• Membranes, Strings and Integrability