On non-commutative N=2 super Yang–Mills

We discuss the Seiberg–Witten solution of the non-commutative N=2 U(N) SYM model. The solution is described in terms of the ordinary Seiberg–Witten curve of the SU(N) theory plus an additional free U(1). Hence, at the two-derivative approximation the theory flows to the ordinary commutative theory in the infrared (k<1/θ ). In particular, the center U(1) is free and it decouples from the other U(1)ʹs. In addition, no UV/IR mixing is found.