Chiral Phase Boundary of QCD from the Functional Renormalization Group

We show how the functional renormalization group can be applied to a study of chiral symmetry breaking in QCD. We discuss the running gauge coupling at finite temperature for QCD. For scales smaller than the corresponding temperature, the coupling is governed by a fixed point of the 3-dimensional theory. Chiral symmetry breaking is approached if the running coupling drives the quark sector to criticality. We analyze the phase boundary in the plane of temperature and number of flavors. For small flavor-numbers, we find good agreement with lattice results. For flavor numbers near the critical flavor number, we find that the scaling of the critical temperature is determined by the zero-temperature IR critical exponent of the running coupling.