QCD phase structure at finite temperature and density

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Understanding the properties and possible phases of strongly-interacting matter under extreme conditions is one of the big challenges of high-energy physics. Hot strongly-interacting matter of several trillion Kelvin was prevalent in the very early universe and similar conditions can be created by colliding heavy ions in particle accelerators, like lead ions at the Large Hadron Collider (LHC) at CERN, Geneva, and gold ions at the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Lab (BNL). On the other hand, densities of the same order of magnitude as present in atomic nuclei can be found in neutron stars, and similar densities are investigated in the Beam Energy Scan program at RHIC and the High Acceptance DiElectron Spectrometer (HADES) as well as the planned Facility for Antiproton and Ion Research (FAIR) of the Gesellschaft für Schwerionenforschung in Darmstadt.Strongly-interacting matter is described by Quantum Chromodynamics (QCD) and its behaviour as a function of temperature and density is summarised in the QCD phase diagram. Although much progress has been made in the last decades, the properties of strongly-interacting matter at intermediate and high densities are still not calculable from first principles.The main objective of this project is a model-parameter free investigation of the phase diagram of QCD. Particular focus will be put on quantities that are accessible to experiments and important for the phenomenological description of heavy-ion collisions. These include fluctuations of conserved charges, which are accessible to heavy-ion collision experiments. Furthermore, the equation of state, which provides an important input for hydrodynamic simulations of the dynamics of heavy-ion collisions, will be computed. These phenomenologically important quantities will be calculated with the help of the functional renormalisation group (FRG) equation. Previous investigations will be generalised to non-vanishing temperatures and densities.