Wilson line correlators in two-dimensional noncommutative Yang-Mills theory

TL;DR

This paper investigates the behavior of Wilson line correlators in two-dimensional noncommutative Yang-Mills theory using perturbative and non-perturbative methods, revealing an exponential growth with momentum.

Contribution

It introduces a combined perturbative and non-perturbative analysis of Wilson line correlators, utilizing Morita equivalence and saddle-point approximation in noncommutative Yang-Mills theory.

Findings

Correlator exhibits exponential increase with momentum p.

Perturbative and non-perturbative results agree in a specific variable region.

Morita equivalence effectively maps open lines to closed Wilson loops.

Abstract

We study the correlator of two parallel Wilson lines in two-dimensional noncommutative Yang-Mills theory, following two different approaches. We first consider a perturbative expansion in the large-N limit and resum all planar diagrams. The second approach is non-perturbative: we exploit the Morita equivalence, mapping the two open lines on the noncommutative torus (which eventually gets decompacted) in two closed Wilson loops winding around the dual commutative torus. Planarity allows us to single out a suitable region of the variables involved, where a saddle-point approximation of the general Morita expression for the correlator can be performed. In this region the correlator nicely compares with the perturbative result, exhibiting an exponential increase with respect to the momentum p.