Understanding the phase structure of Quantum Chromodynamics (QCD) is still one of the major goals in the theoretical and experimental research of matter under extreme conditions. In this context, realistic spectral functions of vector and axial-vector mesons are crucial for identifying signatures of possible phase transitions and critical endpoints in the measured dilepton spectra.In this thesis we calculate the spectral functions of the rho and a1 meson within the Functional Renormalization Group (FRG) approach by using a recently proposed analytic continuation procedure on the level of the flow equations. This is done by employing low-energy effective two-flavor models for QCD in different extensions in which we develop a new formalism to describe fluctuations due to massive (axial-)vector mesons within the FRG. In particular, we study in-medium modifications of these spectral functions in different regions of the phase diagram within the corresponding model where we focus on signatures for a chiral critical endpoint and the restoration of chiral symmetry. Additionally, we calculate temperature- and chemical-potential dependent electromagnetic spectral functions and present a new procedure of solving analytically continued flow equations self-consistently. The feasibility of this procedure is shown by calculating self-consistent spectral functions in the O(4) model.
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