No-Go Theorem for Critical Phenomena in Large-Nc QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, Nc, based on the QCD inequalities and the large-Nc orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential \mu for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential \mu_B = Nc\mu is ruled out, if the coordinate (T, \mu) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential \mu_I = 2\mu.