### 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 |
---|---|

Article number | 121601 |

Journal | Physical Review Letters |

Volume | 108 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2012 Mar 19 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

_{c}QCD.

*Physical Review Letters*,

*108*(12), [121601]. https://doi.org/10.1103/PhysRevLett.108.121601

**No-go theorem for critical phenomena in large-N _{c} QCD.** / Hidaka, Yoshimasa; Yamamoto, Naoki.

Research output: Contribution to journal › Article

_{c}QCD',

*Physical Review Letters*, vol. 108, no. 12, 121601. https://doi.org/10.1103/PhysRevLett.108.121601

_{c}QCD. Physical Review Letters. 2012 Mar 19;108(12). 121601. https://doi.org/10.1103/PhysRevLett.108.121601

}

TY - JOUR

T1 - No-go theorem for critical phenomena in large-N c QCD

AU - Hidaka, Yoshimasa

AU - Yamamoto, Naoki

PY - 2012/3/19

Y1 - 2012/3/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84859027210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859027210&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.108.121601

DO - 10.1103/PhysRevLett.108.121601

M3 - Article

AN - SCOPUS:84859027210

VL - 108

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 12

M1 - 121601

ER -