  We show that in the perturbative regime defined by the coupling constant, the
theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with
or without Supersymmetry-- gives an ordinary gauge theory which is, at the
quantum level, dual to the former. We do so by using the on-shell DeWitt
effective action and dimensional regularization. We explicitly compute the
one-loop two-point function contribution to the on-shell DeWitt effective
action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten
map. We find that the non-local UV divergences found in the propagator in the
Feynman gauge all but disappear, so that they are not physically relevant. We
also show that the quadratic noncommutative IR divergences are gauge-fixing
independent and go away in the Supersymmetric version of the U(1) theory.
