  Noncommutative U(1) gauge theory in 4-dimensions is shown to be equivalent in
some scaling limit to an ordinary non-linear sigma model in 2-dimensions . The
model in this regime is solvable and the corresponding exact beta function is
found. We also show that classical U(n) gauge theory on
{R}^{d-2}{\times}{R}^2_{\theta} can be approximated by a sequence of ordinary
(d-2)-dimensional Georgi-Glashow models with gauge groups U(n(L+1)) where L+1
is the matrix size of the regularized noncommutative plane {R}^2_{\theta}.
