The effect of an infrared divergent quark-antiquark interaction kernel on other Green functions

The n-point Green functions of Landau gauge QCD are systematically investigated in a Dyson-Schwinger approach assuming a static linearly rising potential between fundamental color charges. Besides quarks also scalar matter in the fundamental representation is considered. Starting from the hypothesis of an 1/k^4 infrared divergent matter-antimatter vertex restrictions on the general color tensor structure of this divergence are derived. Consequences for the other four-point functions of QCD, resp., scalar QCD, are presented. Hereby Casimir scaling is found. It is shown that possible singular contributions to the three-point functions vanish due to cancellations within the color algebra. On the other hand, higher n-point functions inherit the infrared singularity of the matter-antimatter vertex in certain color channels. The presented results show that linear confinement is consistently possible in a Greens function approach, however, at the expense that the decoupling theorem is circumvented by infrared singularities.Comment: 7 pages, 2figures, talk presented at the Xth Quark Confinement and the Hadron Spectrum, Munich, Germany, 201

QCD Green's Functions and Phases of Strongly-Interacting Matter

After presenting a brief summary of functional approaches to QCD at vanishing temperatures and densities the application of QCD Green's functions at non-vanishing temperature and vanishing density is discussed. It is pointed out in which way the infrared behavior of the gluon propagator reflects the (de-)confinement transition. Numerical results for the quark propagator are given thereby verifying the relation between (de-)confinement and dynamical chiral symmetry breaking (restoration). Last but not least some results of Dyson-Schwinger equations for the color-superconducting phase at large densities are shown.Comment: 8 pages, 5 figures; talk at the International Workshop on Hot & Cold Baryonic Matter, 15-20 August 2010, Budapest - Hungar

Center Phase Transition from Fundamentally Charged Matter Propagators

The center phase transition at non-vanishing temperatures is investigated in Landau gauge Quantum Chromodynamics (QCD) and scalar QCD. For each theory novel order parameters for the transition are introduced. The matter-gluon vertex which occurs in the Dyson-Schwinger equations of the propagators has to be modeled in contemporary studies. It is found that the nature of the phase transition depends strongly on the detailed structure of this vertex. Our investigation motivates a precise determination of the matter-gluon vertex at non-vanishing temperatures.Comment: 8 pages, Confinement X proceeding

On propagators and vertices of Landau gauge Yang-Mills theory

We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propagator. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agreement with lattice results as well. In turn, these results allow us to assess the effect of the missing two-loop diagrams in the gluon propagator equation. Finally, we present the first self-consistent calculation that includes all two-and three-point functions.Comment: 12 pages, 10 figs., contribution to "QCD-TNT-III: From quarks and gluons to hadronic matter: A bridge too far?", 2-6 Sept 2013, ECT*, Trento, Ital