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Abstract

In this dissertation the phase diagram of hadronic matter is studied. One of its characteristic features is confinement, which denotes the absence of particles with non-zero colour-charge in experimental observations. The fundamental mechanism for confinement is unknown yet, however, there is significant evidence that it is primarily driven by the dynamics of gluons. The interacting system of gluons is called Yang–Mills theory. It is the main focus of this thesis. Functional continuum methods describe the physics via correlation functions, whose thermal behaviour is investigated in this thesis in the framework of the functional renormalisation group. In particular, the temperature-dependent two-point functions are important, since the thermodynamics can be directly accessed by the knowledge of the propagators. In this work this allows for a quantitatively accurate computation of the pressure of Yang–Mills theory. Furthermore, confinement of static quarks is investigated via the Polyakov loop, which is calculated for the gauge groups SU(2) and SU(3) by means of low-order Green functions. Moreover, the effects of dynamical quarks onto the gauge sector are studied. All results are directly compared with findings from other continuum methods and lattice gauge theory.