Renormalization of the Orientable Non-commutative Gross-Neveu Model
  We prove that the non-commutative Gross-Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form "psibar i gamma^{0} gamma^{1} psi". The massless case is renormalizable without such an addition. 
Fabien Vignes-Tourneret