Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory

Abstract

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one- and two- parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynman diagrams, we derive Feynman parameterizations of complicated planar and non-planar Feynman diagrams which simplify their evaluation. For illustration, we compute numerically a four-loop hexagon scalar Feynman diagram.

20 pages, many figures. Two references added. Published version

References in corpus (9)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• On the factorization of overlapping singularities at NNLO
• A Surprise in the Amplitude/Wilson Loop Duality

Cited by in corpus (8)

• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Removing infrared divergences from two-loop integrals
• On the factorization of overlapping singularities at NNLO
• An all order identity between ABJM and N=4 SYM four-point amplitudes
• The One-Loop One-Mass Hexagon Integral in D=6 Dimensions
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• The Wilson-loop $d\log$ representation for Feynman integrals
• Symbols of One-Loop Integrals From Mixed Tate Motives