Perturbative Asymptotic Safety and Its Phenomenological Applications

Asymptotic safety is a remarkable example when fruitful ideas borrowed from statistical physics proliferate to high-energy physics. The concept of asymptotic safety is tightly connected to fixed points (FPs) of the renormalization-group (RG) flow, and generalize well-known asymptotic freedom to a scale-invariant ultraviolet completion with non-vanishing interactions. In this review, we discuss the key ideas behind asymptotic safety, a mechanism for achieving it, and the conditions it imposes on general gauge-Yukawa field theories. We also pay special attention to possible phenomenological applications and provide an overview of standard model (SM) extensions potentially exhibiting asymptotic safety.