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

TL;DR

This paper explores the duality between Wilson loops and scattering amplitudes in N=4 supersymmetric Yang-Mills theory, providing diagrammatic insights and new parameterizations that simplify complex Feynman diagram evaluations.

Contribution

It introduces a diagram-level analysis of the Wilson loop and scattering amplitude duality, deriving Feynman parameterizations for complex diagrams and demonstrating their numerical evaluation.

Findings

One-loop and two-loop diagrams can be expressed as simple parametric integrals.

Two-loop Wilson-loop diagrams correspond to four-loop Feynman diagrams.

Derived new parameterizations that simplify evaluation of complex diagrams.

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.