Equivalence and/or quantum duality of the non/supersymmetric noncommutative field theories related by the theta-exact Seiberg-Witten map

In this article we expound a discovery of the quantum equivalence/duality of U(N) noncommutative quantum field theories (NC QFT) related by the theta-exact Seiberg-Witten (SW) maps and at all orders in the perturbation theory with respect to the coupling constant. We show that this proof holds for Super Yang-Mills (SYM) theories with N=0,1,2,4$ supersymmetry. In short, Seiberg-Witten map does commute with the quantization of the U(N) NCQFT independently, with or without supersymmetry.