The IR/UV connection in non-commutative gauge theories

Quantum field theory on non-commutative spaces does not enjoy the usual ult raviolet-infrared decoupling that forms the basis for conventional renormal ization. The high momentum contributions to loop integrations can lead to u nfamiliar long distance behavior which can potentially undermine naive expe ctations for the IR behavior of the theory. These "anomalies" involve non-a nalytic behavior in the noncommutativity parameter theta making the limit t heta --> 0 singular. In this paper we will analyze such effects in the one loop approximation to gauge theories on non-commutative space. We will see that contrary to expectations poles in theta do occur and lead to large dis crepancies between the expected and actual infrared behavior. We find that poles in theta are absent in supersymmetric theories. The "anomalies" are g enerally still present, but only at the logarithmic level. A notable except ion is non-commutative super Yang-Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.