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

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