A three-loop test of the dilatation operator in N=4 SYM

Abstract

We compute the three-loop anomalous dimension of the BMN operators with charges J=0 (the Konishi multiplet) and J=1 in N=4 super-Yang-Mills theory. We employ a method which effectively reduces the calculation to two loops. Instead of using the superconformal primary states, we consider the ratio of the two-point functions of suitable descendants of the corresponding multiplets. Our results unambiguously select the form of the N=4 SYM dilatation operator which is compatible with BMN scaling. Thus, we provide evidence for BMN scaling at three loops.

38 pages LaTeX, 4 figures, references added

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• The Factorized S-Matrix of CFT/AdS
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Planar N=4 Gauge Theory and the Hubbard Model
• On the highest transcendentality in N=4 SUSY
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Integrability and Transcendentality
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• The Four-Loop Konishi in N=4 SYM
• The Four-Loop Dressing Phase of N=4 SYM
• Five-loop Konishi in N=4 SYM
• Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Towards a string bit formulation of N=4 super Yang-Mills
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Towards Baxter equation in supersymmetric Yang-Mills theories
• Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
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• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Spin Chain for Quantum Strings
• Operator mixing in N=4 SYM: The Konishi anomaly revisited
• A two-loop test for the factorised S-matrix of planar N=4
• Baxter equation for long-range SL(2|1) magnet
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Anomalous dimensions of leading twist conformal operators
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• Operator Mixing and the AdS/CFT correspondence
• Non-perturbative contributions to the plane-wave string mass matrix
• Aspects of Integrability in AdS/CFT Duality
• A wide class of four point functions of BPS operators in N=4 SYM at order g^4
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
• Finite size corrections and integrability of $\mathcal{N}=2$ SYM and DLCQ strings on a pp-wave
• Finite-size corrections to the rotating string and the winding state
• Non-planar anomalous dimension of twist-2 operators: higher moments at four loops
• Wrapping Interactions and the Konishi Operator
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• Form factors with two operator insertions and the principle of maximal transcendentality
• On twist-two operators in N=4 SYM
• Scrambling in Yang-Mills
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
• On the breakdown of perturbative integrability in large N matrix models
• Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Wrapping effects in supersymmetric gauge theories
• Three-loop universal anomalous dimension of the Wilson operators in N=4 Supersymmetric Yang-Mills theory
• Rationality of the Anomalous Dimensions in N=4 SYM theory
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Operator mixing in N = 4 SYM: The Konishi anomaly re-re-visited
• Infrared structure of $\mathcal{N}$ = 4 SYM and leading transcendentality principle in gauge theory