Two loop integrability for Chern-Simons theories with N=6 supersymmetry

Abstract

We consider two-loop anomalous dimensions for fermionic operators in the ABJM model and the ABJ model. We find the appropriate Hamiltonian and show that it is consistent with a previously predicted Bethe ansatz for the ABJM model. The difference between the ABJ and ABJM models is invisible at the two-loop level by cancelation of parity violating diagrams. We then construct a Hamiltonian for the full two-loop OSp(6|4) spin chain by first constructing the Hamiltonian for an SL(2|1) subgroup, and then lifting to OSp(6|4). We show that this Hamiltonian is consistent with the Hamiltonian found for the fermionic operators.

23 pages, 4 figures; v2: minor misprints corrected, reference added

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• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• AdS4/CFT3 at One Loop
• Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory
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• Comment on the Scaling Function in AdS4 x CP3
• Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
• Semi-classical strings in AdS_4*CP^3
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• Finite Size Giant Magnon
• Integrable Spin Chain of Superconformal U(M)xU(N) Chern-Simons Theory
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• Spiky Strings on AdS(4) X CP**3
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Baxter Q-operator for graded SL(2|1) spin chain
• Heisenberg spin chains based on sl(2|1) symmetry
• A note on the reduction of the AdS4 x CP3 string sigma model
• Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory
• Giant Magnon and Spike Solutions with Two Spins in AdS4xCP3
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Exact Solution of a Electron System Combining Two Different t-J Models
• Zero Modes for the Boundary Giant Magnons

Cited by in corpus (70)

• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Anomalous radius shift in AdS(4)/CFT(3)
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• Generation of Matrix Models by W-operators
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• Long-Range Deformations for Integrable Spin Chains
• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)
• Worldsheet spectrum in AdS(4)/CFT(3) correspondence
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• Magnon dispersion to four loops in the ABJM and ABJ models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Unitary Integrals and Related Matrix Models
• One Loop Amplitudes In ABJM
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Infrared Stability of N=2 Chern-Simons Matter Theories
• A note on amplitudes in N=6 superconformal Chern-Simons theory
• Marginal Deformations and 3-Algebra Structures
• Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory
• Scattering in ABJ theories
• Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
• One-Loop Corrections to Type IIA String Theory in AdS4 x CP3
• Correlation functions of magnon and spike
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Non-planar ABJ Theory and Parity
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• On the Exact Interpolating Function in ABJ Theory
• Spin Chains in N=2 Superconformal Theories: from the Z_2 Quiver to Superconformal QCD
• On wrapping corrections to GKP-like operators
• Correlation function of dyonic strings
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• Dressed Giant Magnons on CP^3
• Giant Magnons on CP^3 by Dressing Method
• The worldsheet low-energy limit of the AdS_4 x CP^3 superstring
• All one-loop amplitudes in N=6 superconformal Chern-Simons theory
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• Finite size effect on the magnon's correlation functions
• Perturbative Stability along the Supersymmetric Directions of the Landscape
• Integrated negative geometries in ABJM
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• Factorized Tree-level Scattering in AdS_4 x CP^3
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• The Morphology of N=6 Chern-Simons Theory
• On three-point functions in ABJM and the latitude Wilson loop
• Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories
• Two-Loop Spectroscopy of Short ABJM Operators
• Scattering of Giant Magnons in CP^3
• Symplectic Three-Algebra and N=6, Sp(2N) X U(1) Superconformal Chern-Simons-Matter Theory
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• The Leading Order Dressing Phase in ABJM Theory
• Spin chain for the deformed ABJM theory
• Nonplanar Integrability and Parity in ABJ Theory
• On the absence of reflection in AdS4/CFT3
• On thermodynamics of N=6 superconformal Chern-Simons theory
• Y-system for $\gamma$-deformed ABJM Theory
• Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories
• Integrability of Orbifold ABJM Theories
• Correlation functions of the ABJM model
• Notes on BPS Wilson Loops and the Cusp Anomalous Dimension in ABJM theory
• Wrapping effects in supersymmetric gauge theories
• Fermionic reductions of the AdS4 x CP3 superstring
• Neumann-Rosochatius system for strings in ABJ Model
• A limit on the ABJ model