Annales Henri Poincaré

, Volume 8, Issue 3, pp 427-474

First online:

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Renormalization of the Orientable Non-commutative Gross–Neveu Model

  • Fabien Vignes-TourneretAffiliated withLaboratoire de Physique Théorique Bât. 210, CNRS UMR 8627, Université Paris XI Email author 


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 \(\bar{\psi}\imath\gamma^{0}\gamma^{1}\psi\). The massless case is renormalizable without such an addition.