Quantum Critical Behaviour of Semisimple Gauge Theories

We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an SUðNÞ gauge theory with M Dirac flavors where we gauge first an SUðMÞL and then an SUð2ÞL ⊂ SUðMÞL of the original global symmetry SUðMÞL × SUðMÞR × Uð1Þ of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop 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 renormalization 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 safety
free trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics à la walking is investigated.