Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion

TL;DR

This paper investigates the behavior of Wilson loops in two-dimensional noncommutative Euclidean gauge theories, revealing anomalous effects at high noncommutativity and proposing regularization methods via the noncommutative loop equation.

Contribution

It introduces a perturbative expansion formula for Wilson loops in noncommutative gauge theories and analyzes their anomalous behavior at large noncommutativity parameters.

Findings

Perturbative expansion formula derived for Wilson loops.

Anomalous behavior observed at high noncommutativity.

Regularization schemes constructed using the noncommutative loop equation.

Abstract

We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise general formula and demonstrate its anomalous behavior at large parameter of noncommutativity for the simplest nonplanar diagram of genus 1. We discuss various UV/IR regularizations of the two-dimensional noncommutative gauge theory in the axial gauge and, using the noncommutative loop equation, construct a consistent regularization.