Two-dimensional non-commutative Yang-Mills theory: coherent effects in open Wilson line correlators

TL;DR

This paper computes and resums the perturbative correlator of three parallel open Wilson lines in two-dimensional non-commutative U(N) gauge theory, revealing an exponential growth with line length despite interference effects.

Contribution

It provides the first perturbative calculation and resummation of three-line Wilson line correlators in 2D non-commutative gauge theory, extending previous two-line results.

Findings

Correlator exhibits exponential growth with line length.

Interference effects do not suppress the exponential increase.

Results likely extend to multiple lines sharing the same orientation.

Abstract

A perturbative calculation of the correlator of three parallel open Wilson lines is performed for the U(N) theory in two non-commutative space-time dimensions. In the large-N planar limit, the perturbative series is fully resummed and asymptotically leads to an exponential increase of the correlator with the lengths of the lines, in spite of an interference effect between lines with the same orientation. This result generalizes a similar increase occurring in the two-line correlator and is likely to persist when more lines are considered provided they share the same direction.