One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

Abstract

We compute at the one-loop order the beta-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 beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.

16 pages, 9 figures

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Cited by in corpus (15)

• Vacuum configurations for renormalizable non-commutative scalar models
• On the vacuum states for noncommutative gauge theory
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Quantum gauge theories on noncommutative 3-d space
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Duality covariant quantum field theory on noncommutative Minkowski space
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Noncommutative Induced Gauge Theories on Moyal Spaces
• Connes distance by examples: Homothetic spectral metric spaces
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model