The case against asymptotic freedom

TL;DR

This paper reviews 15 years of research challenging the widely accepted belief that nonabelian symmetry theories like nonlinear sigma models and Yang-Mills are asymptotically free, presenting evidence against this notion.

Contribution

It provides a comprehensive overview of evidence collected over 15 years that questions the asymptotic freedom property in nonabelian symmetry theories.

Findings

Evidence against asymptotic freedom in nonlinear sigma models

Evidence against asymptotic freedom in Yang-Mills theories

Challenging the conventional understanding of nonabelian gauge theories

Abstract

In this talk I give an overview of the work done during the last 15 years in collaboration with the late Adrian Patrascioiu. In this work we accumulated evidence against the commonly accepted view that theories with nonabelian symmetry -- either two dimensional nonlinear $\sigma$ models or four dimensional Yang-Mills theories -- have the property of asymptotic freedom (AF) usually ascribed to them.