No-go theorem for critical phenomena in large-N _c QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N _c, based on the QCD inequalities and the large-N _c 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 μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ _B=N _cμ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ _I=2μ.