The quark propagators of QCD and QCD-like theories

We investigate the phase structures of theories which differ from QCD only in the gauge group and can be simulated on the lattice at non-vanishing chemical potential $\mu$. These theories can thus serve as testing ground for functional methods at non-vanishing density. We determine the chiral and confinement/deconfinement transitions at $\mu =0$ for the three gauge groups $SU(3)$, $SU(2)$ and $G_2$ for two quark flavors and extend the study of the chiral transition to non-zero $\mu$. We locate the critical point where the chiral crossover becomes a real phase transition. Within the employed truncation, we find that all three theories behave qualitatively very similarly.