The hadronic SU(3) Parity Doublet Model for Dense Matter, its extension   to quarks and the strange equation of state
  A chiral model is introduced that is based on the parity doublet formulation of chiral symmetry including hyperonic degrees of freedom. The phase structure of the model is determined. Depending on the masses of the chiral partners the transition to the chirally restored phase shows a first-order line with critical endpoints as function of chemical potential and temperature in additional to the standard liquid-gas phase transition of self-bound nuclear matter. We extend the parity doublet model to describe the deconfinement phase transition which is in quantitative agreement with lattice data at $\mu_B=0$. The phase diagram of the model is presented which shows a decoupling of chiral symmetry restoration and deconfinement. Loosening the constraint of strangeness conservation we also investigate the phase diagram at net strangeness density. We calculate the strangeness per baryon fraction and the baryon strangeness correlation factor, two quantities that are sensitive on deconfinement and that can be used to interpret lattice calculations. 
J. Steinheimer, S. Schramm, H. St\"ocker
hep-ph