### Abstract

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 _{c}μ 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.

Original language | English |
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Article number | 121601 |

Journal | Physical review letters |

Volume | 108 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2012 Mar 19 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Hidaka, Y., & Yamamoto, N. (2012). No-go theorem for critical phenomena in large-N

_{c}QCD.*Physical review letters*,*108*(12), [121601]. https://doi.org/10.1103/PhysRevLett.108.121601