Magnon dispersion to four loops in the ABJM and ABJ models

Abstract

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.

LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram corrected: modified result in the ABJ case only, formulations improved, typos fixed, references added; v3: signs of three diagrams corrected, modifying the final result

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Cited by in corpus (50)

• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Exact Slope and Interpolating Functions in ABJM Theory
• Chern-Simons-Matter Theory
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• Y-system and Quasi-Classical Strings
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Non-conformality of gamma_i-deformed N=4 SYM theory
• One Loop Amplitudes In ABJM
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Exact Bremsstrahlung functions in ABJM theory
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Spin Chains in N=2 Superconformal Theories: from the Z_2 Quiver to Superconformal QCD
• On wrapping corrections to GKP-like operators
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• On semiclassical calculation of three-point functions in AdS_4 x CP^3
• Aspects of ABJ Theory
• Non-anticommutative ABJ Theory
• Integrated negative geometries in ABJM
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories
• ABJM quantum spectral curve and Mellin transform
• Two-Loop Spectroscopy of Short ABJM Operators
• Scattering of Giant Magnons in CP^3
• On thermodynamics of N=6 superconformal Chern-Simons theory
• On the absence of reflection in AdS4/CFT3
• Y-system for $\gamma$-deformed ABJM Theory
• Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations
• An exact limit of ABJM
• Notes on BPS Wilson Loops and the Cusp Anomalous Dimension in ABJM theory
• Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Correlation functions of the ABJM model
• ABJM flux-tube and scattering amplitudes
• Wrapping effects in supersymmetric gauge theories
• Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton
• Exact Results in Supersymmetric Gauge Theories
• Large J expansion in ABJM theory revisited
• A limit on the ABJ model
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations