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

Abstract

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 μfor any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ_B = Ncμis 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.

5 pages, 1 figure; published version