The quark propagator in QCD and $G_2$ QCD

QCD-like theories provide testing grounds for truncations of functional equations at non-zero density, since comparisons with lattice results are possible due to the absence of the sign problem. As a first step towards such a comparison, we determine for QCD and $G_2$ QCD the chiral and confinement/deconfinement transitions from the quark propagator Dyson-Schwinger equation at zero chemical potential by calculating the chiral and dual chiral condensates, respectively.