Regular Article - Theoretical Physics
One-loop beta functions for the orientable non-commutative Gross–Neveu model
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
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Published online: 2 October 2007
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.
© Springer-Verlag / Società Italiana di Fisica, 2007