Nuclear matter Hagedorn Phase Quarkyonic Phase! QGP (Deconfined phase) Sp(N) Hadronic Phase (Vacuum) Mesonic phase Baryonic phase Strangeness O(N) SU(N) Color-flavor-coupling Color-neutral Colored QGP Non-singlet-state Color-singlet Temperature (T) 1 2 3 Internal color structure exponent: , B FIG. 4: (Color online) Same as Fig. (1). The complexity of the Hagedorn bag’s internal structure is proportional to µ$_{B}$ and is inverse proportional to T . When µ$_{B}$ becomes sufficient large, the color and flavor degrees of freedom are coupled to each other and form Sp ( N ) symmetry group. The complexity of the color-flavor symmetry and space configuration symmetry increases as the system is cooled down and extremely compressed to large µ$_{B}$ . 69