Quantum Critical Behaviour of Semi-Simple Gauge Theories

TL;DR

This paper explores the phase diagram of semi-simple gauge theories similar to the Standard Model, revealing multiple fixed points, asymptotic freedom, and safety free trajectories with potential phenomenological implications.

Contribution

It provides a detailed perturbative analysis of the phase structure of semi-simple fermionic gauge theories, uncovering novel fixed points and RG trajectories not previously characterized.

Findings

Existence of phases with multiple fixed points

Discovery of safety free trajectories with coupled asymptotic behaviors

Potential for near-conformal dynamics in phenomenology

Abstract

We study the perturbative phase diagram of semi-simple fermionic gauge theories resembling the Standard Model. We investigate an $SU(N)$ gauge theory with $M$ Dirac flavors where we gauge first an $SU(M)_L$ and then an $SU(2)_L \subset SU(M)_L$ of the original global symmetry $SU(M)_L\times SU(M)_R \times U(1) $ of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalisation group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are \emph{safety free} trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics a l\'a walking is investigated.