Theorems for Asymptotic Safety of Gauge Theories

TL;DR

This paper classifies fixed points in gauge theories, emphasizing the role of Yukawa couplings, and derives conditions for their asymptotic safety, impacting understanding of phase diagrams and beyond Standard Model physics.

Contribution

It provides a comprehensive classification of fixed points and establishes necessary and sufficient conditions for asymptotic safety in gauge theories.

Findings

Identification of conditions for asymptotic safety

Classification of high- and low-energy fixed points

Implications for phase diagrams and BSM physics

Abstract

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.