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We investigate quantum chromodynamics with two colors at nonvanishing density using Dyson-Schwinger equations. Lattice methods do not have a complex action problem in this theory. Thus, we can benchmark our results and the effect of truncations directly by comparing with the corresponding lattice results. We do so for the gluon propagator, the chiral condensate, and the quark number density and test variations of the employed truncation to improve the agreement. Finally, we compare the effect of a truncation on the chiral and confinement/deconfinement transitions in the phase diagrams of QCD and QCD with the gauge groups $SU(2)$ and $G_2$., Comment: 12 pages, 10 figures; agrees with published version

We perform a semi-perturbative calculation of the quark-gluon vertex inspired from the three-loop expanded 3PI effective action and investigate the relative strengths of the chirally symmetric/broken tensor structures below and above the crossover., Comment: 7 pages, 4 figures, submitted to proceedings of Excited QCD 2018, 11-15 March 2018, Kopaonik, Serbia

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., Comment: 6 pages, 3 figures, submitted to proceedings of Excited QCD 2017, 7-13 May 2017, Sintra, Portugal

We investigate the universality of truncation schemes for Dyson-Schwinger equations developed for quantum chromodynamics in theories which differ from quantum chromodynamics only in the gauge group. Our specific choices are the gauge groups $SU(2)$ and $G_2$, for which lattice calculations at nonvanishing chemical potential are possible. Thus, corresponding calculations can provide benchmarks for testing calculations with functional equations. We calculate the quark and gluon propagators and determine the chiral and dual chiral condensates at vanishing density to determine the confinement/deconfinement and chiral transitions, respectively. We can reproduce the expected type of transitions in the quenched and unquenched cases. In general, all three theories react very similarly to modifications of the employed model for the quark-gluon vertex., Comment: 13 pages, 12 figs; v3: corresponds to published version; added figure of quark mass, updated numbers for transition temperatures based on an improved interpolation in temperature, adapted quark masses to match lattice calculations

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., Comment: 7 pages, 6 figures, submitted to proceedings of 'XIIth Quark Confinement and the Hadron Spectrum', August 28-September 04, 2016, Thessaloniki, Greece