Structural stability of the RG flow in the Gross-Neveu model

TL;DR

This paper investigates the non-perturbative renormalization group flow of the massless Gross-Neveu model in two dimensions, demonstrating stability properties and establishing an ultraviolet stability bound using a novel application of existing methods.

Contribution

It applies a method originally developed for infrared problems to analyze the ultraviolet stability of the RG flow in the Gross-Neveu model, providing new insights into its non-perturbative behavior.

Findings

Quadratic approximation to the flow remains bounded after renormalization.

Complete flow remains bounded for weak coupling.

Ultraviolet stability bound is proven for the model.

Abstract

We study flow of renormalization group (RG) transformations for the massless Gross-Neveu model in a non-perturbative formulation. The model is defined on a d=2 dimensional Euclidean space with a finite volume. The quadratic approximation to the flow stays bounded after suitable renormalization. We show that for weak coupling this property also is true for the complete flow. As an application we prove an ultraviolet stability bound for the model. Our treatment is an application of a method of Bauerschmidt, Brydges, and Slade. The method was developed for an infrared problem, and is now applied to an ultraviolet problem.