  We perform a non-perturbative study of pure gauge theory in a two dimensional
non-commutative (NC) space. On the lattice, it is equivalent to the twisted
Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe
a clear large-N scaling for the 1- and 2-point function of Wilson loops, as
well as the 2-point function of Polyakov lines. The 2-point functions agree
with a universal wave function renormalization. Based on a Morita equivalence,
the large-N double scaling limit corresponds to the continuum limit of NC gauge
theory, so the observed large-N scaling demonstrates the non-perturbative
renormalizability of this NC field theory. The area law for the Wilson loops
holds at small physical area as in commutative 2d planar gauge theory, but at
large areas we find an oscillating behavior instead. In that regime the phase
of the Wilson loop grows linearly with the area. This agrees with the
Aharonov-Bohm effect in the presence of a constant magnetic field, identified
with the inverse non-commutativity parameter.
