Large \(N_c\) QCD phase diagram at \(\mu _B=0\)

Lattice studies suggest that at zero baryon chemical potential and increasing temperature there are three characteristic regimes in QCD that are connected by smooth analytical crossovers: a hadron gas regime at \(T < T_{ch}\sim 155\) MeV, an intermediate regime, called stringy fluid, at \(T_{ch}< T < \sim 3 T_{ch}\), and a quark-gluon plasma regime at higher temperatures. These regimes have been interpreted to reflect different approximate symmetries and effective degrees of freedom. In the hadron gas the effective degrees of freedom are hadrons and the approximate chiral symmetry of QCD is spontaneously broken. The intermediate regime has been interpreted as lacking spontaneous chiral symmetry breaking along with the emergence of new approximate symmetry, chiral spin symmetry, that is not a symmetry of the Dirac Lagrangian, but is a symmetry of the confining part of the QCD Lagrangian. While the high temperature regime is the usual quark-gluon plasma which is often considered to reflect “deconfinement” in some way. This paper explores the behavior of these regimes of QCD as the number of colors in the theory, \(N_c\), gets large. In the large \(N_c\) limit the theory is center-symmetric and notions of confinement and deconfinement are unambiguous. The energy density is \(\mathcal{O}(N_c^0)\) in the meson gas, \({{\mathcal {O}}}(N_c^1)\) in the intermediate regime and \({{\mathcal {O}}}(N_c^2)\) in the quark-gluon plasma regime. In the large \(N_c\) limit these regimes may become distinct phases separated by first order phase transitions. The intermediate phase has the peculiar feature that glueballs should exist and have properties that are unchanged from what is seen in the vacuum (up to \(1/N_c \) corrections), while the ordinary dilute gas of mesons with broken chiral symmetry disappears and approximate chiral spin symmetry should emerge.