Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory

Abstract

We report a calculation in N = 4 Yang-Mills of the four-loop term g^4 in the collinear anomalous dimension g(lambda) which governs the universal subleading infrared structure of gluon scattering amplitudes. Using the method of obstructions to extract this quantity from the 1/epsilon singularity in the four-gluon iterative relation at four loops, we find g^4 = -1240.9 with an estimated numerical uncertainty of 0.02%. We also analyze the implication of our result for the strong coupling behavior of g(lambda), finding support for the string theory prediction computed recently by Alday and Maldacena using AdS/CFT.

5 pages, 2 figures

References in corpus (34)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Gluon scattering amplitudes at strong coupling
• Cuba - a library for multidimensional numerical integration
• A semi-classical limit of the gauge/string correspondence
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Automatized analytic continuation of Mellin-Barnes integrals
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• The Factorized S-Matrix of CFT/AdS
• Multi-loop Amplitudes and Resummation
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Structure functions for large $x$ and renormalization of Wilson loops
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Nonperturbative Corrections in Resummed Cross Sections
• Anomalous dimensions of Wilson operators in N=4 SYM theory
• A note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• The Four-Loop Dressing Phase of N=4 SYM
• Hidden Beauty in Multiloop Amplitudes

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• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
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• Generating AdS String Solutions
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• The Four Loop QCD Rapidity Anomalous Dimension
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• New Dual Conformally Invariant Off-Shell Integrals
• Duality between Wilson loops and gluon amplitudes
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Planar quark scattering at strong coupling and universality
• The virtual scaling function of AdS/CFT
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Some properties of the Alday-Maldacena minimum
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Full-color three-loop three-point form factors in N=4 SYM
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Dressing the Giant Gluon
• Twistor actions for gauge theory and gravity
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• Cross-Order Integral Relations from Maximal Cuts
• Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Sum rules for higher twist sl(2)operators in N=4 SYM
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• Deviation from Alday-Maldacena Duality For Wavy Circle
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• The nonplanar cusp and collinear anomalous dimension at four loops in $\mathcal{N}=4$ SYM theory
• On-shell Methods for Form Factors in N=4 SYM and Their Applications