Thermodynamics of dense matter in chiral approaches

We discuss phases in dense hadronic and quark matter from chiral model approaches. Within PNJL models the phase diagram for various number of colors $N_c$ is studied. How phases are constrained in quantum field theories are also discussed along with the anomaly matching. An exotic phase with unbroken center symmetry of chiral group has a characteristic feature in the thermodynamics, which can be interpreted as one realization of the quarkyonic phase in QCD for $N_c=3$.

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