Gauge theory webs and surfaces

TL;DR

This paper explores the geometric interpretation of Wilson line polygons in gauge theories, linking renormalization scales with invariant distances through two-dimensional integrals expressed as exponentials.

Contribution

It introduces a geometric framework for understanding Wilson line polygons and their renormalization in gauge theories using coordinate space integrals.

Findings

Expressed Wilson line polygons as exponentials of 2D integrals.

Linked renormalization scales with invariant distances geometrically.

Provided a new perspective on gauge theory Wilson lines.

Abstract

We analyze the perturbative cusp and closed polygons of Wilson lines for massless gauge theories in coordinate space, and express them as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link renormalization scales with invariant distances.