Nonlinear sigma model and Yang-Mills theory through non-critical string

TL;DR

This paper explores the connection between the nonlinear sigma model and Yang-Mills theory using non-critical string holography, revealing their coupled renormalization group flows and asymptotic freedom.

Contribution

It demonstrates a dual relation of coupling constants and analyzes the simultaneous RG flows of both theories within a non-critical string framework.

Findings

Coupled RG flows of sigma model and Yang-Mills theory identified

Dual relation of coupling constants established

Asymptotic freedom of Yang-Mills confirmed

Abstract

We consider two-dimensional nonlinear sigma model from the viewpoint of the holography, which has been applied to the study of the Yang-Mills theory, based on the non-critical string theory. We can see the renormalization group flows for both the nonlinear sigma model and the Yang-Mills theory at the same time, and the two theories are intimately related through a kind of dual relation of the coupling constants. We address the running behaviors of these coupling constants and also the asymptotic freedom of the Yang-Mills theory.