Gliding down the QCD transition line, from $N_f=2$ till the onset of conformality

Abstract: We review the hot QCD transition with varying number of flavors, from two till the onset of the conformal window. We discuss the universality class for $N_f=2$, along the critical line for two massless light flavors, and a third flavor whose mass serves as an interpolator between $N_f = 2$ and $N_f=3$. We identify a possible scaling window for the 3D $O(4)$ universality class transition, and its crossover to a mean field behaviour. We follow the transition from $N_f=3$ to larger $N_f$, when it remains of first order, with an increasing coupling strength; we summarize its known properties, including possible cosmological applications as a model for a strong electroweak transition. The first order transition, and its accompanying second order endpoint, finally morphs into the essential singularity at the onset of the conformal window, following the singular behaviour predicted by the Functional Renormalization Group.