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

TL;DR

This paper calculates the one-loop beta-functions for a non-commutative version of the Gross-Neveu model on the Moyal plane, revealing asymptotic freedom for any number of colors and a non-zero beta-function for the Thirring model counterpart.

Contribution

It provides the first one-loop beta-function calculations for a non-commutative Gross-Neveu model, demonstrating asymptotic freedom in this setting.

Findings

Non-commutative Gross-Neveu model is asymptotically free for any number of colors.

Beta-function for the non-commutative Thirring model is non-zero.

Calculation performed using x-space formalism.

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.