QCD strings and the thermodynamics of the metastable phase of QCD at large $N_c$

Abstract

The thermodyanmics of a metastable hadronic phase of QCD at large $N_C$ are related to properties of an effective QCD string. In particular, it is shown that in the large $N_c$ limit and near the maximum hadronic temperature, $T_H$, the energy density and pressure of the metastable phase scale as $\mathcal{E}\sim (T_H-T{)}^{-(D_{\perp }-6)/2}$ (for $D_{\perp }<6$) and $P\sim (T_H-T{)}^{-(D_{\perp }-4)/2}$ (for $D_{\perp }<4$) where $D_{\perp }$ is the effective number of transverse dimensions of the string theory. It is shown, however, that for the thermodynamic quantities of interest the limits $T\to T_H$ and $N_c\to \infty$ do not commute. The prospect of extracting $D_{\perp }$ via lattice simulations of the metastable hadronic phase at moderately large $N_c$ is discussed.

Comments: After this paper was published, the author became aware of an important early paper by Charles Thorn on the subject of the QCD phase transition at large N_c and its relation to the Hagedorn spectrum. Given the pioneering nature of Thorn's paper, and the fact that it is not as widely known as it should be, it is important to cite it in the present work. This updated version cites Thorn's work