We argue that the whole or the part of the phase diagrams of QCD and QCD-like
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 region 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.Comment: v1: 35 pages, 6 figures; v2: 37 pages, 6 figures, minor improvements,
conclusion unchanged; v3: version published in JHE
