Quantum Chromodyamics (QCD) is the quantum field theory of strong interactions, which have quarks and gluons as their fundamental degrees of freedom. QCD plays a crucial role in describing phenomena ranging from the early universe to forces within nuclei, which make up the world around us. The exploration of the phase diagram of strongly interacting matter is a scientific challenge a lot of effort is put in from experimental as well as theoretical groups around the globe.In this thesis, we explore the phase diagram of QCD using chiral effective models within the non-perturbative framework of the functional renormalization group (FRG). We use the two-flavor quark-meson model as an effective model for low- energy QCD, calculating its phase diagram as well as quark spectral functions, which are obtained from analytically continued RG flow equations. For modelling nuclear matter we use a chiral baryon-meson model, the so-called parity-doublet model, which allows for the baryons to acquire a Dirac mass term without breaking chiral symmetry. This model can describe the liquid-gas transition of nuclear matter together with chiral symmetry restoration in the high baryon density phase and will be considered in the extended mean-field approximation as well as including mesonic and fermionic fluctuations using the FRG.
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