Working With Wilson Lines

TL;DR

This paper introduces an algorithm that simplifies the calculation of Wilson lines on piecewise linear paths by relating different topologies through their color structure, enabling efficient comparisons.

Contribution

It provides a novel method to express Wilson lines in terms of their segments, reducing computational complexity and facilitating topology comparisons.

Findings

Reduces the number of diagrams needed for calculations.

Enables easy switching between different Wilson line topologies.

Improves efficiency in testing various Wilson line structures.

Abstract

We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that different linear path topologies can be related to each other using their color structure. This framework allows one to easily switch results between different Wilson line topologies, which is helpful when testing different structures against each other.