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

TL;DR

This paper explores the thermodynamics of a metastable QCD phase at large N_c, linking it to properties of an effective QCD string, and discusses how lattice simulations could determine the string's transverse dimensions.

Contribution

It establishes a relationship between the thermodynamics of metastable QCD phases and effective string theory, highlighting the non-commuting limits of temperature and N_c, and proposes lattice methods to determine string dimensions.

Findings

Energy density and pressure scale near T_H with specific exponents depending on D_perp.

Limits T → T_H and N_c → ∞ do not commute for thermodynamic quantities.

Potential to extract D_perp from lattice simulations of the metastable phase.

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 ${\cal E} \sim (T_H-T)^{-(D_\perp-6)/2}$ (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.