Conformal Phase Diagram of Complete Asymptotically Free Theories

TL;DR

This paper analyzes the fixed point structure of gauge-Yukawa theories to identify conditions for complete asymptotic freedom and the existence of infrared stable fixed points, revealing special trajectories with combined safety and conformality.

Contribution

It provides the first comprehensive conditions for complete asymptotic freedom and uncovers special trajectories where couplings are both safe and conformal.

Findings

Derived conditions for asymptotic freedom and infrared fixed points.

Identified special trajectories with both asymptotic safety and conformality.

Mapped the fixed point structure of gauge-Yukawa theories.

Abstract

We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.