Abstract :
We study the U(N) non-commutative Yang–Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the θ→0 limit of the U(N) theory does not converge to the ordinary SU(N)×U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.
