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A chiral model is introduced that is based on the parity doublet formulationof chiral symmetry including hyperonic degrees of freedom. The phase structureof the model is determined. Depending on the masses of the chiral partners thetransition to the chirally restored phase shows a first-order line withcritical endpoints as function of chemical potential and temperature inadditional to the standard liquid-gas phase transition of self-bound nuclearmatter. We extend the parity doublet model to describe the deconfinement phasetransition 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 chiralsymmetry restoration and deconfinement. Loosening the constraint of strangenessconservation we also investigate the phase diagram at net strangeness density.We calculate the strangeness per baryon fraction and the baryon strangenesscorrelation factor, two quantities that are sensitive on deconfinement and thatcan be used to interpret lattice calculations.

The hadronic SU(3) Parity Doublet Model for Dense Matter, its extension to quarks and the strange equation of state