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

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 and resum all planar diagrams, planarity acquiring a meaning in two dimensions only in the large-N limit. 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.