Wilson lines on noncommutative tori

Abstract

We introduce the notion of a monodromy for gauge fields with vanishing curvature on the noncommutative torus. Similar to the ordinary gauge theory, traces of the monodromies define noncommutative Wilson lines. Our main result is that these Wilson lines are invariant under the Seiberg-Witten map changing the deformation parameter of the noncommutative torus.Comment: 4 pages, LaTeX (revtex), it is explained why the costruction of a Wilson line using the path ordered exponent does not apply in the noncommutative cas