The Renormalization Group Approach to the Confining String

TL;DR

This paper applies the renormalization group framework to non-abelian gauge theories, connecting string sigma models with gauge coupling evolution, and demonstrates the universality of the string vacuum geometry in reproducing Yang-Mills beta functions.

Contribution

It introduces a renormalization group approach to string representations of gauge theories, showing the universality of the string vacuum geometry and its relation to Yang-Mills beta functions.

Findings

Reproduces Yang-Mills beta function to all orders in perturbation theory.

Establishes a universal intrinsic geometry for the string vacuum.

Studies tachyon stability, glueball mass gap, and Wilson loop area law.

Abstract

The renormalization group approach towards the string representation of non abelian gauge theories translates, in terms of the string sigma model beta function equations, the renormalization group evolution of the gauge coupling constant and Zamolodchikov`s $c$ function. Tachyon stability, glueball mass gap, renormalization group evolution of the $c$ function and the area law for the Wilson loop are studied for a critical bosonic string vacuum corresponding to a non abelian gauge theory in four dimensional space-time. We prove that the same intrinsic geometry for the string vacuum is universal in some sense, reproducing the Yang-Mills beta function to arbitrary loop order in perturbation theory.