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 ψ̄γ⁰γ¹ψ . The massless case is renormalizable without such an addition.