The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals

Abstract

Correlation functions of Wilson lines are relevant for describing the infrared structure of scattering amplitudes. We develop a new method for evaluating a wide class of such Wilson line integrals, and apply it to the calculation of the velocity-dependent cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. We compute the four-loop non-planar correction in a recently introduced scaling limit. Moreover, we derive the full planar four-loop result by means of an ansatz which is based on the structure of known analytic results. We determine the coefficients in this ansatz by making use of a relationship to massive scattering amplitudes. As a corollary, our analytical result confirms the four-loop value of the light-like cusp anomalous dimension. Finally, we use the available perturbative data, as well as insight from AdS/CFT, in order to extrapolate the leading order values at strong coupling. The latter agree within two per cent with the corresponding string theory result, over a wide range of parameters.

29 pages, 5 figures. Title modified, sections 2 and 4 extended, references added. Matches published version

References in corpus (27)

• Multiloop integrals in dimensional regularization made simple
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Comments on operators with large spin
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Color-kinematic Duality for Form Factors
• Generalized quark-antiquark potential at weak and strong coupling
• The cusp anomalous dimension at three loops and beyond
• Four-Loop Cusp Anomalous Dimension From Obstructions
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Quark-antiquark potential in AdS at one loop
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops
• Cusped SYM Wilson loop at two loops and beyond
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Systematics of the cusp anomalous dimension
• The static potential in {\cal N}=4 supersymmetric Yang-Mills at weak coupling
• Ladders for Wilson Loops Beyond Leading Order
• NLL resummation for the static potential in N=4 SYM theory
• Topics in Cusped/Lightcone Wilson Loops

Cited by in corpus (55)

• Lectures on differential equations for Feynman integrals
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Exact Bremsstrahlung and Effective Couplings
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• On the Casimir scaling violation in the cusp anomalous dimension at small angle
• Localization and AdS/CFT Correspondence
• Master integrals for the four-loop Sudakov form factor
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• From Webs to Polylogarithms
• Soft anomalous dimensions for single-top production at three loops
• Adequate bases of phase space master integrals for $gg\to h$ at NNLO and beyond
• Webs and Posets
• Multiple Gluon Exchange Webs
• Subleading Regge limit from a soft anomalous dimension
• Multiparton webs beyond three loops
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Wilson loops in terms of color invariants
• An Introduction to Webs
• Cwebs beyond three loops in multiparton amplitudes
• Cross-Order Integral Relations from Maximal Cuts
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Three-loop cusp anomalous dimension and a conjecture for $n$ loops
• Imaginary parts and discontinuities of Wilson line correlators
• Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
• Dyson equations for correlators of Wilson loops
• A factorization approach to next-to-leading-power threshold logarithms
• Ladder Limit for Correlators of Wilson Loops
• Exact N${}^3$LO results for $q{q}^{\prime }\to H+X$
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Position-space cuts for Wilson line correlators
• Cusped Wilson lines in symmetric representations
• Four-loop QCD cusp anomalous dimension at small angle
• QCD cusp anomalous dimension: current status
• The nonplanar cusp and collinear anomalous dimension at four loops in $\mathcal{N}=4$ SYM theory
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair
• The Standard Model from the LHC to future colliders: a contribution to the Workshop "What Next" of INFN
• Wilson Loops and Integrability
• On the cusp anomalous dimension in the ladder limit of $\mathcal{N}=4$ SYM
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics
• Progress on the infrared structure of multi-particle gauge theory amplitudes
• On interpolating anomalous dimension of twist-two operators with general spins
• Boomerang webs up to three-loop order
• Progress on soft gluon exponentiation and long-distance singularities