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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.
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We note that the phase diagram at finite μ B \mu_{B} qualitatively changes from ordinary nuclear matter or color superconductivity to some exotic phases as a function of N c N_{c} inside the pion condensed phase in the corresponding phase diagram of QCD at finite μ I \mu_{I} [ 8 , 9 ] : baryon crystal [ 10 ] , inhomogeneous chiral density wave [ 8 ] , or quarkyonic chiral spiral phase [ 11 ] is realized instead (see also [ 12 ] ). Although 1 / N c 1/N_{c} expansion may not be useful in this low- T T nuclear domain, the chiral phase transition at high T T is similar, at least qualitatively, between large- N c N_{c} and N c = 3 N_{c}=3 outside the pion condensed phase
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Y. Hidaka and N. Yamamoto, in preparation
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