Renormalization of the Orientable Non-commutative Gross-Neveu Model

TL;DR

This paper proves the all-order renormalizability of the non-commutative Gross-Neveu model on the 2D Moyal plane, addressing UV/IR mixing issues and identifying necessary counterterms in the massive case.

Contribution

It demonstrates the renormalizability of the non-commutative Gross-Neveu model and specifies the additional counterterm needed for the massive case.

Findings

Model is renormalizable to all orders.

UV/IR mixing persists but does not prevent renormalizability.

Additional counterterm required in the massive case.

Abstract

We prove that the non-commutative Gross-Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form "psibar i gamma^{0} gamma^{1} psi". The massless case is renormalizable without such an addition.