Eur. Phys. J. C (2007) 52: 735-742
https://doi.org/10.1140/epjc/s10052-007-0424-2

Regular Article - Theoretical Physics

One-loop beta functions for the orientable non-commutative Gross–Neveu model

¹ Laboratoire de Physique Théorique, Université Paris XI, Bât. 210, 91405, Orsay Cedex, France
² IHÉS, Le Bois-Marie, 35 route de Chartres, 91440, Bures-sur-Yvette, France

^* e-mail: jean-christophe.wallet@th.u-psud.fr

Received: 27 March 2007
Published online: 2 October 2007

Abstract

We compute at the one-loop order the β-functions for a renormalisable non-commutative analog of the Gross–Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.