Strong coupling phenomena on the non-commutative plane

We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, we make use of a T-dual description in terms of an N → ∞ limit of U(N) gauge theory on a commutative torus. The magnetic flux on this torus is taken to be m = N − 1, while the area scales like 1/N, keeping ΛQCD fixed. With a few assumptions, we argue that the speed of high frequency light in pure non-commutative QED is modified in the non-commutative directions by the factor ΛQCD4 θ2, provided ΛQCD2 θ >> 1. If charged flavors are included, there is an upper bound on the momentum of a photon propagating in the non-commutative directions, beyond which it is unstable against production of charged pairs. We also discuss a particular θ→∞ limit of pure non-commutative QED which is T-dual to a more conventional N→∞ limit with m/N fixed. In the non-commutative description, this limit gives rise to an exotic theory of open strings.