Noncommutative N=1,2 super U(N) Yang–Mills: UV/IR mixing and effective action results at one loop

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 consider contributions to the effective action 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.