Noncommutative gauge theory, divergences and closed strings

We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared diverg ences resulting from integrating out high momentum modes. In order to repro duce the correct infrared behaviour, the wilsonian effective action has to include certain "closed string" modes with prescribed couplings. In the cas e of quiver gauge theories, realized in string theory on orbifolds, we iden tify the required modes with a set of twisted sector fields. These closed s tring modes have exactly the prescribed couplings to correct the wilsonian effective action. This provides a concrete origin for the appearance of clo sed string modes in noncommutative field theories.