Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field

TL;DR

This paper proves that the beta function of the Grosse-Wulkenhaar model with a magnetic field is zero at all perturbation orders, indicating a fixed point in the renormalization group flow.

Contribution

It demonstrates the all-order vanishing of the beta function for the Grosse-Wulkenhaar model with magnetic field and identifies a non-Gaussian infrared fixed point.

Findings

Beta function vanishes at all perturbation orders.

Identification of a non-Gaussian infrared fixed point.

Discussion of implications for the model's behavior.

Abstract

We prove that the beta function of the Grosse-Wulkenhaar model including a magnetic field vanishes at all order of perturbations. We compute the renormalization group flow of the relevant dynamic parameters and find a non-Gaussian infrared fixed point. Some consequences of these results are discussed.