Nuclear matter Hagedorn Phase Quarkyonic Phase! QGP (Deconfined phase) CFL color-super conductivity non-CFL quark liquid Hadronic Phase (Vacuum) RHIC Mesonic phase Baryonic phase Strangeness More- complex-flavor- structure Color-flavor coupling Color-neutral Color non-singlet Colored SU(N) Color-singlet Temperature (T) Baryonic chemical potential B FIG. 2: (Color online) Same as Fig. (1). The hadronic phases those are dominated by the mesonic, baryonic and strangeness phases are depicted explicitly. It is shown that the complexity of the Hagedorn state internal color-flavor structure increases with respect to µ$_{B}$ . The mesonic Hagedorn states are dominated at small µ$_{B}$ while the baryonic and excited Hagedorn states appear abundantly as the µ$_{B}$ increases and when µ$_{B}$ becomes significantly large the Hagedorn states with strangeness and more other complicated degrees of freedom emerge in the system. The ∗ (blue online) indicates the color-singlet U (1) N$_{c}$ states (Hagedorns) with the unimodular-like constraint. 67