QCD phase structure at finite temperature and density

We discuss the phase structure of QCD for N-f = 2 and N-f = 2 + 1 dynamical quark flavors at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate out quantum fluctuations toward low energies by using the functional renormalization group. By dynamically hadronizing the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for mu(B)/T less than or similar to 6. We find a critical endpoint at (T-CEP; mu(BCEP))= (107; 635) MeV. The curvature of the phase boundary at small chemical potential is. = 0.0142o2THORN, computed from the renormalized light chiral condensate.l;R. Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for mu(B) greater than or similar to 417 MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation toward a quantitatively precise determination of QCD phase diagram.