A Consistent Noncommutative Field Theory: the Wess-Zumino Model
  We show that the noncommutative Wess-Zumino model is renormalizable to all orders of perturbation theory. The noncommutative scalar potential by itself is non-renormalizable but the Yukawa terms demanded by supersymmetry improve the situation turning the theory into a renormalizable one. As in the commutative case, there are neither quadratic nor linear divergences. Hence, the IR/UV mixing does not give rise to quadratic infrared poles. 
H. O. Girotti, M. Gomes, V. O. Rivelles and A. J. da Silva