A non perturbative approach of the principal chiral model between two and four dimensions

TL;DR

This paper introduces a non-perturbative Wilson-like renormalization group method to analyze the principal chiral model across two to four dimensions, resolving previous discrepancies in perturbative approaches.

Contribution

It presents a novel non-perturbative approach to study the principal chiral model across multiple dimensions without small parameter expansions.

Findings

Identified the three-dimensional critical physics of the model.

Resolved discrepancies between different perturbative methods.

Tracked the evolution of effective coupling constants across dimensions.

Abstract

We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.