We argue that the whole or the part of the phase diagrams of QCD and QCDlike theories should be universal in the large-N c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N c) QCD at finite isospin chemical potential and SO(2N c) and Sp(2N c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover regions in these theories, the phase diagrams are also identical to that of SU(N c) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.
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