Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond

Abstract

We study issues concerning perturbative integrability of N=6 Chern-Simons theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics, we derive so called maximal-ranged interactions in the quantum dilatation generator, originating from homogeneous and inhomogeneous diagrams. These diagrams require proper regularization of not only ultraviolet but also infrared divergences. We first consider standard operator mixing method. We show that homogeneous diagrams are obtainable by recursive method to all orders. The method, however, is not easily extendable to inhomogeneous diagrams. We thus consider two-point function method and study both operator contents and spectrum of the quantum dilatation generator up to six loop orders. We show that, of two possible classes of operators, only one linear combination actually contributes. Curiously, this is exactly the same combination as in N=4 super Yang-Mills theory. We then study spectrum of anomalous dimension up to six loops. We find that the spectrum agrees perfectly with the prediction based on quantum integrability. In evaluating the six loop diagrams, we utilized remarkable integer-relation algorithm (PSLQ) developed by Ferguson, Baily and Arno.

1+39 pages, 12 figures, references added, minor structural changes, typos corrected

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• Fractional M2-branes
• Giant Magnons
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• The Bethe ansatz for superconformal Chern-Simons
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• The AdS4/CFT3 algebraic curve
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• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
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• Non-planar ABJ Theory and Parity
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Cited by in corpus (16)

• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• Infrared Stability of N=2 Chern-Simons Matter Theories
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• The worldsheet low-energy limit of the AdS_4 x CP^3 superstring
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• Two-Loop Spectroscopy of Short ABJM Operators
• Thermal Aspects of ABJM theory: Currents and Condensations
• Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories
• Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential
• Static Length Scales of N=6 Chern-Simons Plasma
• Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory