We relate quark confinement, as measured by the Polyakov-loop order parameter, to color confinement, as described by the Kugo-Ojima/Gribov-Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and
gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) -- in agreement with general expectations. As an estimate for the critical temperature, we obtain T_c=284MeV for SU(3).
We study the phase diagram of QCD with the help of order parameters for chiral symmetry breaking and quark confinement. We also introduce a new order parameter for the confinement phase transition, which is related to the quark density. It is easily
accessible by different theoretical approaches, such as functional approaches or lattice simulations. Its relation to the Polyakov loop expectation value is discussed and the QCD phase diagram is analysed. Our results suggest a close relation between the chiral and the confinement phase transition.
We derive the two-loop effective action for covariantly constant field strength of pure Yang-Mills theory in the presence of an infrared scale. The computation is done in the framework of the worldline formalism, based on a generalization procedure o
f constructing multiloop effective actions in terms of the bosonic worldline path integral. The two-loop beta-function is correctly reproduced. This is the first derivation in the worldline formulation, and serves as a nontrivial check on the consistency of the multiloop generalization procedure in the worldline formalism.
