The relation between the deconfinement and chiral phase transition is explored in the framework of an Polyakov-loop-extended two-flavor quark-meson (PQM) model. In this model the Polyakov loop dynamics is represented by a background temporal gauge field which also couples to the quarks. As a novelty an explicit quark chemical potential and N f -dependence in the Polyakov loop potential is proposed by using renormalization group arguments. The behavior of the Polyakov loop as well as the chiral condensate as function of temperature and quark chemical potential is obtained by minimizing the grand canonical thermodynamic potential of the system. The effect of the Polyakov loop dynamics on the chiral phase diagram and on several thermodynamic bulk quantities is presented.

Chiral symmetry restoration at nonzero temperature and quark densities are investigated in the framework of a linear sigma model with N f = 3 light quark flavors. After the derivation of the grand potential in mean-field approximation, the nonstrange and strange condensates, the in-medium masses of the scalar and pseudoscalar nonets are analyzed in hot and dense medium. The influence of the axial anomaly on the nonet masses and the isoscalar mixings on the pseudoscalar η-η ′ and scalar σ(600)-f0(1370) complex are examined. The sensitivity of the chiral phase transition as well as the existence and location of a critical end point in the phase diagram on the value of the sigma mass is explored. The chiral critical surface with and without the influence of the axial U (1)A anomaly is elaborated as a function of the pion and kaon masses for several values of the sigma mass.

The Polyakov-extended quark-meson model (PQM) is investigated beyond mean-field. This represents an important step towards a fully dynamical QCD computation. Both the quantum fluctuations to the matter sector and the back-reaction of the matter fluctuations to the QCD Yang-Mills sector are included. Results on the chiral and confinement-deconfinement crossover/phase transition lines and the location of a possible critical endpoint are presented. Moreover, thermodynamic quantities such as the pressure and the quark density are discussed.

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Based on the proper-time renormalization group approach, the scalar and the quark number susceptibilities in the vicinity of possible critical end points of the hadronic phase diagram are investigated in the two-flavor quark-meson model. After discussing the quark-mass dependence of the location of such points, the critical behavior of the in-medium meson masses and quark number density are calculated. The universality classes of the end points are determined by calculating the critical exponents of the susceptibilities. In order to numerically estimate the influence of fluctuations we compare all quantities with results from a mean-field approximation. It is concluded that the region in the phase diagram where the susceptibilities are enhanced is more compressed around the critical end point if fluctuations are included.

The Polyakov-quark-meson (PQM) model, which combines chiral as well as deconfinement aspects of strongly interacting matter is introduced for three light quark flavors. An analysis of the chiral and deconfinement phase transition of the model and its thermodynamics at finite temperatures is given. Three different forms of the effective Polyakov loop potential are considered. The findings of the 2 + 1 flavor model investigations are confronted to corresponding recent QCD lattice simulations of the RBC-Bielefeld, HotQCD and Wuppertal-Budapest collaborations. The influence of the heavier quark masses, which are used in the lattice calculations, is taken into account. In the transition region the bulk thermodynamics of the PQM model agrees well with the lattice data.

The idea of the functional renormalization group and one-loop improved renormalization group flows are reviewed. The associated flow equations and nonperturbative approximations schemes for its solutions are discussed. These techniques are then applied to the strong interaction in the framework of an effective quark meson model which is introduced in great detail. The renormalization group analysis of the two flavor quark meson model is extended to finite temperature and quark chemical potential which allows for an analysis of the chiral phase diagram beyond the mean field approximation.

We introduce a two-flavor quark-meson-diquark model for two-color QCD and its extensions to include gauge-field dynamics as described by the Polakov loop. Grand potential and phase structure are being studied both in mean-field approximation and with the functional renormalization group. The model provides an explicit example for the importance of baryonic degrees of freedom: When they are omitted, the phase diagram closely resembles that of the corresponding (Polyakov)-quark-meson models for QCD, in particular including their critical endpoint. In order to reproduce the well established main features based on the symmetries and breaking patterns of two-color QCD, however, they must be included and there is no critical endpoint. The competing dynamics of collective mesonic and baryonic fluctuations is well described by the functional renormalization group equation in lowest order derivative expansion for the effective potential which we solve numerically on a two-dimensional grid in field space.Comment: 22 pages, pdflatex, 11 pdf figures; v2: minor revisions to the text, one additional figure, accepted for publication in PR