German Title: Zum Phasendiagramm der QCD

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Abstract

In this thesis we study two flavour Quantum Chromodynamics (QCD) with the Functional Renormalisation Group (FRG). We compute the QCD phase diagram at imaginary and real chemical potential in the chiral limit. We introduce dual order parameters which originate in the matter sector but are sensitive to center symmetry breaking. For real and imaginary chemical potential we find that the chiral and the confinement–deconfinement transitions agree. At vanishing chemical potential we obtain for the chiral transition Tc = 181 MeV and for the confinement–deconfinement crossover Tc ≈ 178 MeV. The dual density and the Polyakov loop agree within the percent level. At imaginary chemical potential the phase dia- gram shows the expected Roberge–Weiss periodicity. This constitutes the first calculation of the QCD phase diagram at imaginary chemical potential in the chiral limit. At real chemical potential our results agree with lattice, DSE and FRG model studies. Then we compare the Yang–Mills (YM) and the glue Polyakov loop potential and match the temperature scales as the matter contributions to the gauge dynamics do not alter the form of the potential but the temperature scale. We use the translation of the two temperature scales in a Polyakov Quark Meson model, where we study the order parameters and the thermodynamic observables. The Polyakov loop potential thus approximates the glue dynamics instead of the YM dynamics. We find very good agreement for the thermodynamic observables with lattice results.