  We show the universality of phase diagrams in QCD and QCD-like theories
through the large-N_c equivalence. The whole phase diagrams are identical
between QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c)
gauge theories at finite baryon chemical potential. In the chiral limit, they
are also identical to that of QCD at finite chiral chemical potential. Outside
the pion or diquark condensed phase in these theories, the universality of
phase diagrams is applicable to QCD at finite baryon chemical potential. We
further argue that the universality may work approximately even for N_c=3. Our
result makes it possible to study QCD at finite baryon chemical potential and
high temperature, especially the chiral phase transition, using sign-free
theories on the lattice.
