The IR/UV connection in non-commutative gauge theories

Abstract

Quantum field theory on non-commutative spaces does not enjoy the usual ultraviolet-infrared decoupling that forms the basis for conventional renormalization. The high momentum contributions to loop integrations can lead to unfamiliar long distance behavior which can potentially undermine naive expectations for the IR behavior of the theory. These "anomalies" involve non-analytic behavior in the noncommutativity parameter θ making the limit θ → 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 θ do occur and lead to large discrepancies between the expected and actual in-frared behavior. We find that poles in θ are absent in supersymmetric theories. The "anomalies" are generally still present, but only at the logarithmic level. A notable exception is non-commutative super Yang-Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.