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 Tc ≃ 284MeV for SU(3).

The theory of the strong interaction, Quantum Chromodynamics (QCD), describes the generation of hadronic masses and the state of hadronic matter during the early stages of the evolution of the universe. As a complement, experiments with ultracold fermionic atoms provide a clean environment to benchmark our understanding of dynamical formation of condensates and the generation of bound states in strongly interacting many-body systems.Renormalization group (RG) techniques offer great potential for theoretical advances in both hot and dense QCD as well as many-body physics, but their connections have not yet been investigated in great detail. We aim to take a further step to bridge this gap. A cross-fertilization is indeed promising since it may eventually provide us with an ab-initio description of hadronization, condensation, and bound-state formation in strongly interacting theories. After giving a thorough introduction to the derivation and analysis of fermionic RG flows, we give an introductory review of our present understanding of universal long-range behavior in various different theories, ranging from non-relativistic many-body problems to relativistic gauge theories, with an emphasis on scaling behavior of physical observables close to quantum phase transitions (i. e. phase transitions at zero temperature) as well as thermal phase transitions.

We study the phase diagram of two flavour QCD at imaginary chemical potential in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analysed with a new order parameter for the confinement phase transition. We show that it is directly related to both, the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.

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We present an analysis of the dynamics of two-flavour QCD in the vacuum. Special attention is paid to the transition from the high energy quark-gluon regime to the low energy regime governed by hadron dynamics. This is done within an functional renormalisation group approach to QCD amended by dynamical hadronisation techniques. The latter allow us to describe conveniently the transition from the perturbative high-energy regime to the nonperturbative low-energy limit without suffering from a fine-tuning of model parameters. In the present work, we apply these techniques to two-flavour QCD with physical quark masses and show how the dynamics of the dominant low-energy degrees of freedom emerge from the underlying quark-gluon dynamics.