Two-flavor QCD at finite temperature and chemical potential in a functional approach

We summarize recent results obtained in the Dyson-Schwinger formalism to study the chiral and deconfinement phase transitions of quenched and unquenched QCD at finite temperature and chemical potential. In the quenched case we compare SU(2) and SU(3) gauge theories by taking lattice data for the gluon as an input for the quark Dyson-Schwinger equation. As compared to previous investigations we find a clearer distinction between the second order transition of the two-color theory and the (weak) first order transition of the three-color gauge theory. We then extend this study to unquenched QCD at finite chemical potential by taking matter effects to the gluon into account and investigate the order of the chiral phase transition and the behavior of the deconfinement transition. What we find are coinciding phase transitions up to a critical endpoint which is located at large chemical potential.