Renormalization Group Flow in a General Gauge Theory

TL;DR

This paper analyzes the renormalization group flow in general gauge theories, revealing the asymptotic behavior and classifying flow patterns based on a bounded potential in 3+1 dimensions.

Contribution

It provides a comprehensive analysis of RG flow in general gauge theories with a simple gauge group, introducing a classification of flow patterns and their asymptotic structures.

Findings

Flow of Yukawa and gauge couplings described by a bounded potential

Classification of possible RG flow patterns

Insights into the asymptotic structure of gauge theories

Abstract

The renormalization group flow in a general renormalizable gauge theory with a simple gauge group in 3+1 dimensions is analyzed. The flow of the ratios of the Yukawa couplings and the gauge coupling is described in terms of a bounded potential, which makes it possible to draw a number of non-trivial conclusions concerning the asymptotic structure of the theory. A classification of possible flow patterns is given.