QCD at finite temperature and density within the fRG approach: An overview

In this paper we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group (fRG) approach. The fRG is a nonperturbative continuum field approach, in which quantum, thermal and density fluctuations are integrated in successively with the evolution of the renormalization group (RG) scale. The fRG results for the QCD phase structure and the location of the critical end point (CEP), the QCD equation of state (EoS), the magnetic EoS, baryon number fluctuations confronted with recent experimental measurements, various critical exponents, spectral functions in the critical region, the dynamical critical exponent, etc., are presented. Recent estimates of the location of the CEP from first-principle QCD calculations within fRG and Dyson-Schwinger Equations, which passes through lattice benchmark tests at small baryon chemical potentials, converge in a rather small region at baryon chemical potentials of about 600 MeV. A region of inhomogeneous instability indicated by a negative wave function renormalization is found with $\mu_B\gtrsim 420$ MeV. It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments, could arise from the increasingly sharp crossover in the regime of low collision energy.