Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills

Abstract

BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in N=4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N, and make contact with the string worldsheet description at strong coupling. As an application of our results, we compute exactly a small-angle limit (and more generally near-BPS limits) of the cross anomalous dimension which governs the UV divergence of intersecting Wilson lines. The same quantity describes the soft anomalous dimension of scattering amplitudes of W-bosons in the Coulomb branch.

arXiv comment45 pages; v2 references added

References in corpus (59)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Supersymmetric Wilson loops on S^3
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Hexagonalization of Correlation Functions
• Defects in conformal field theory
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• High energy scattering in QCD and cross singularities of Wilson loops
• Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
• Bootstrapping the QCD soft anomalous dimension
• 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model
• The cusp anomalous dimension at three loops and beyond
• Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
• Wilson loops: From four-dimensional SYM to two-dimensional YM
• Loop Equations and bootstrap methods in the lattice
• On near forward high energy scattering in QCD
• Gauge fields - strings duality and the loop equation
• 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
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Exact null octagon
• Notes on supersymmetric Wilson loops on a two-sphere
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
• Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in $Ad{S}_5\times S^5$
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Clustering and the Three-Point Function
• Bremsstrahlung function, leading Luscher correction at weak coupling and localization
• Wilson loop for large N Yang-Mills theory on a two-dimensional sphere
• The Octagon as a Determinant
• Correlators of supersymmetric Wilson loops at weak and strong coupling
• Loop dynamics and AdS/CFT correspondence
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Wilson loop on a sphere
• Precision matching of circular Wilson loops and strings in AdS(5)xS(5)
• Spin chain integrability in non-supersymmetric Wilson loops
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
• Positivity of hexagon perturbation theory
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Wilson Loops in Large N QCD on a Sphere
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• A New Type of Loop Equations
• Dyson equations for correlators of Wilson loops
• Ladder Limit for Correlators of Wilson Loops
• Emitted Radiation and Geometry
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory

Cited by in corpus (2)

• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve