### Hadrons under extreme conditions

The properties of a large number of hadrons in vacuum (mass, decay-width, spin, etc.) are by now quite well known and understood from experimental measurements and theoretical studies. What however happens if one puts these hadrons in a very hot and/or dense environment, is still a matter of ongoing research and only few established facts are available at present. Studying this question can be relevant for interpreting the experimental findings of heavy ion collision experiments at BNL or CERN, where an extremely hot environment is created, or to understand astrophysical objects such as neutron stars, which at their centers are believed to be many times more dense than normal nuclear matter. Our goal is hence to understand the modification of hadrons under such extreme conditions from the fundamental theory of the strong interaction, namely quantum chromo dynamics (QCD) and especially to study the relation of hadronic properties under extreme conditions to the realization of the various symmetries of QCD in a particular environment.

**Spectral functions and in-medium properties of hadrons**

The properties of strong-interaction matter at high temperatures and densities are of central interest to ongoing theoretical as well as experimental efforts. From an experimental point of view, information on the medium-modifications of hot hadronic matter can for example be extracted from dilepton invariant mass spectra, as measured within relativistic heavy-ion collisions. The theoretical description of such spectra is based on in-medium spectral functions of hadrons, in particular of the light vector-mesons.

The calculation of real-time quantities like spectral functions at finite temperature and chemical potential is, however, often difficult. Lattice QCD, for example, not only suffers from the sign-problem at finite chemical potential, but also faces the analytic continuation problem, which describes the difficulty to extract information on real-time observables from Euclidean imaginary-time correlation functions.

At ECT* (Ralf-Arno Tripolt, Jochen Wambach), we are developing a new method to calculate real-time quantities like spectral functions and transport coefficients at finite temperature and chemical potential. This method is based on the non-perturbative Functional Renormalization Group (FRG) framework and involves an analytic continuation on the level of the flow equations. It has successfully been applied to the quark-meson model, where we have calculated mesonic spectral functions in different regimes of the corresponding phase diagram, in particular near the critical endpoint. Using the momentum-dependent spectral functions as input, we were also able to calculate the shear viscosity to entropy density ratio.

Our future research aims include the calculation of (axial-) vector meson spectral functions will allow us calculate the resulting dilepton spectra. In this context, also the inclusion of baryonic degrees of freedom represents an exciting extension of our approach. This will allow for a more realistic description of the high-chemical-potential and low-temperature regime of the QCD phase diagram.