Cusped SYM Wilson loop at two loops and beyond

Abstract

We calculate the anomalous dimension of the cusped Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to order ${\lambda }^2$ ($\lambda =g_{YM}^{2}N$). We show that the cancellation between the diagrams with the three-point vertex and the self-energy insertion to the propagator which occurs for smooth Wilson loops is not complete for cusped loops, so that an anomaly term remains. This term contributes to the cusp anomalous dimension. The result agrees with the anomalous dimensions of twist-two conformal operators with large spin. We verify the loop equation for cusped loops to order ${\lambda }^2$, reproducing the cusp anomalous dimension this way. We also examine the issue of summing ladder diagrams to all orders. We find an exact solution of the Bethe-Salpeter equation, summing light-cone ladder diagrams, and show that for certain values of parameters it reduces to a Bessel function. We find that the ladder diagrams cannot reproduce for large $\lambda$ the $\sqrt{\lambda }$-behavior of the cusp anomalous dimension expected from the AdS/CFT correspondence.

32pp., Latex, 6 figures

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• Generalized quark-antiquark potential at weak and strong coupling
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• The cusp anomalous dimension at three loops and beyond
• 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
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
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• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• Supersymmetric Wilson loops at two loops
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• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Localization and AdS/CFT Correspondence
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Systematics of the cusp anomalous dimension
• Anomalous Dimensions from a Spinning D5-Brane
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• Ladders for Wilson Loops Beyond Leading Order
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Evolution of cusped light-like Wilson loops and geometry of the loop space
• Resumming planar diagrams for the N=6 ABJM cusped Wilson loop in light-cone gauge
• Holographic dual of defect CFT with corner contributions
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• On the cusp anomalous dimension in the ladder limit of $\mathcal{N}=4$ SYM
• Generalised cusp anomalous dimension in beta-deformed super Yang Mills theory
• Topics in Cusped/Lightcone Wilson Loops
• Numerical Prediction of cusps or kinks in the Nambu-Goto dynamics
• Wilson Loops and Integrability
• Wilson loops as defects in N=2 conformal field theories
• Generalized quark-antiquark potential in AdS/CFT