Universality of phases in QCD and QCD-like theories

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.