Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of   quadratic noncommutative IR divergences
  We compute the one-loop 1PI contributions to all the propagators of the noncommutative N=1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the means of the theta-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator. 
Carmelo P. Martin, Josip Trampetic and Jiangyang You
hep-th math-ph math.MP