Noncommutative N=1 and N=2 supersymmetric Yang-Mills theories with gauge group U(N) are studied here using the background field method and superspace background covariant D-algebra in perturbation theory. At one loop divergences arise only in the two-point functions. They are logarithmic UV/IR divergences in the planar/nonplanar sectors that play a role dual to each other. We compute the planar and non planar contributions to the three- and four-point functions with vector external lines. We find that the three-point function vanishes, while the four-point function receives contributions both from vector and from chiral matter loops.
@article{arxiv.hep-th/0012009,
title = {Noncommutative ${\cal N}=1,2$ super U(N) Yang-Mills: UV/IR mixing and effective action results at one loop},
author = {Daniela Zanon},
journal= {arXiv preprint arXiv:hep-th/0012009},
year = {2014}
}