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

TL;DR

This paper proves that critical phenomena and phase transitions are forbidden in large-Nc QCD under certain conditions, using rigorous inequalities and orbifold equivalence, especially ruling out the critical point at finite baryon chemical potential.

Contribution

It establishes a no-go theorem for critical phenomena in large-Nc QCD, extending the understanding of phase structure constraints using rigorous theoretical tools.

Findings

Critical phenomena are forbidden in flavor-symmetric large-Nc QCD at finite T and  not too large.

The critical point at finite baryon chemical potential _B is ruled out outside the pion condensed phase.

The results are based on QCD inequalities and large-Nc orbifold equivalence.

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 \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.