  We study the quantum mechanical consistency of noncommutative gauge theories
by perturbatively analyzing the Wilsonian quantum effective action in the
matrix formulation. In the process of integrating out UV states, we find new
divergences having dual UV-IR interpretations and no analogues in ordinary
quantum field theories. The appearance of these new UV-IR divergences has
profound consequences for the renormalizability of the theory. In particular,
renormalizability fails in any nonsupersymmetric noncommutative gauge theory.
In fact, we argue that renormalizability generally fails in any noncommutative
theory that allows quantum corrections beyond one-loop. Thus, it seems that
noncommutative quantum theories are extremely sensitive to the UV, and only the
softest UV behavior can be tolerated.
