Price of Asymptotic Safety

TL;DR

This paper argues that weakly coupled fixed points in four-dimensional quantum field theories require non-abelian gauge interactions, impacting theories in particle physics and conformal field theory.

Contribution

It demonstrates that theories without gauge interactions cannot reliably have weakly coupled fixed points, highlighting the essential role of gauge interactions in asymptotic safety.

Findings

Weakly coupled fixed points require non-abelian gauge interactions.

The absence of gauge interactions prevents reliable fixed points in 4D QFTs.

Implications for particle physics and conformal field theory are discussed.

Abstract

All known examples of four dimensional quantum field theories with asymptotic freedom or asymptotic safety at weak coupling involve non-abelian gauge interactions. We demonstrate that this is not a coincidence: no weakly coupled fixed points, ultraviolet or otherwise, can be reliably generated in theories lacking gauge interactions. Implications for particle physics, critical phenomena, and conformal field theory are indicated.