### Abstract

We argue that the whole or the part of the phase diagrams of QCD and QCDlike theories should be universal in the large-N _{c} limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N _{c}) QCD at finite isospin chemical potential and SO(2N _{c}) and Sp(2N _{c}) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover regions in these theories, the phase diagrams are also identical to that of SU(N _{c}) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.

Original language | English |
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Article number | 138 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Mar 12 |

Externally published | Yes |

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### Keywords

- 1/N expansion
- Matrix models
- QCD

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(2), [138]. https://doi.org/10.1007/JHEP02(2012)138