Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions

TL;DR

This paper computes exact correlation functions of open Wilson lines in two-dimensional noncommutative Yang-Mills theory, revealing insights into weak and strong coupling regimes through topological and group-theoretic expansions.

Contribution

It provides the first exact expressions for open Wilson line correlators in noncommutative 2D Yang-Mills, linking instanton and algebraic expansions to physical regimes.

Findings

Exact correlation functions expressed in two forms

Weak-coupling limit derived from topological instanton expansion

Strong-coupling and high-momentum behaviour analyzed via group theory

Abstract

The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only topological numbers of Heisenberg modules and enables extraction of the weak-coupling limit of the gauge theory. A dual algebraic expansion involves only group theoretic quantities, winding numbers and translational zero modes, and enables analysis of the strong-coupling limit of the gauge theory and the high-momentum behaviour of open Wilson lines. The dual expressions can be interpreted physically as exact sums over contributions from virtual electric dipole quanta.