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

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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.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Université Paris XI, Bât. 210, 91405, Orsay Cedex, France

    A. Lakhoua & J.-C. Wallet

  2. IHÉS, Le Bois-Marie, 35 route de Chartres, 91440, Bures-sur-Yvette, France

    F. Vignes-Tourneret

Authors
  1. A. Lakhoua
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  2. F. Vignes-Tourneret
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  3. J.-C. Wallet
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Correspondence to A. Lakhoua.

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Lakhoua, A., Vignes-Tourneret, F. & Wallet, JC. One-loop beta functions for the orientable non-commutative Gross–Neveu model . Eur. Phys. J. C 52, 735–742 (2007). https://doi.org/10.1140/epjc/s10052-007-0424-2

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  • DOI: https://doi.org/10.1140/epjc/s10052-007-0424-2

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