Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories

Abstract

In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.

LaTeX, feynmp, 70 pages; v2: signs of three diagrams due to inconsistent Feynman rules corrected, modifying the final result, typos corrected, formulations improved

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• The Bethe ansatz for superconformal Chern-Simons
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• Anomalous dimension with wrapping at four loops in N=4 SYM
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Magnon dispersion to four loops in the ABJM and ABJ models
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
• Non-planar ABJ Theory and Parity
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond

Cited by in corpus (56)

• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Magnon dispersion to four loops in the ABJM and ABJ models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Wronskian Solution for AdS/CFT Y-system
• 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
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Non-conformality of gamma_i-deformed N=4 SYM theory
• One Loop Amplitudes In ABJM
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Two-loop cusp anomaly in ABJM at strong coupling
• Exact Bremsstrahlung functions in ABJM theory
• Scattering in ABJ theories
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• On the Exact Interpolating Function in ABJ Theory
• The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• An all order identity between ABJM and N=4 SYM four-point amplitudes
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• On wrapping corrections to GKP-like operators
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Form Factors of Chiral Primary Operators at Two Loops in ABJ(M)
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• Integrated negative geometries in ABJM
• The a-function in three dimensions: beyond leading order
• ABJ(M) Chiral Primary Three-Point Function at Two-loops
• On three-point functions in ABJM and the latitude Wilson loop
• ABJM quantum spectral curve and Mellin transform
• Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
• Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• The Leading Order Dressing Phase in ABJM Theory
• The a-function for N=2 supersymmetric gauge theories in three dimensions
• The tricritical Ising CFT and conformal bootstrap
• Y-system for $\gamma$-deformed ABJM Theory
• An exact limit of ABJM
• Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations
• An Extremal Chiral Primary Three-Point Function at Two-loops in ABJ(M)
• Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential
• Correlation functions of the ABJM model
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Integrable systems and AdS/CFT duality
• Wrapping effects in supersymmetric gauge theories
• Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton
• Supergraphs and the cubic Leigh-Strassler model
• Superconformal Chern-Simons theories beyond leading order
• A note on scattering amplitudes on the moduli space of ABJM
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations