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We argue that the whole or the part of the phase diagrams of QCD and QCD-liketheories should be universal in the large-N_c limit through the orbifoldequivalence. The whole phase diagrams, including the chiral phase transitionsand the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finiteisospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finitebaryon chemical potential. Outside the BEC-BCS crossover region in thesetheories, the phase diagrams are also identical to that of SU(N_c) QCD atfinite baryon chemical potential. We give examples of the universality in somesolvable cases: (i) QCD and QCD-like theories at asymptotically high densitywhere the controlled weak-coupling calculations are possible, (ii) chiralrandom matrix theories of different universality classes, which are solvablelarge-N (large volume) matrix models of QCD. Our results strongly suggest thatthe chiral phase transition and the QCD critical point at finite baryonchemical potential can be studied using sign-free theories, such as QCD atfinite isospin chemical potential, in lattice simulations.

Universality of Phases in QCD and QCD-like Theories