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.

arXiv commentAfter 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

References in corpus (7)

• Hadron Resonance Mass Spectrum and Lattice QCD Thermodynamics
• Thermodynamics at Non-Zero Baryon Number Density: A Comparison of Lattice and Hadron Resonance Gas Model Calculations
• Properties of the deconfining phase transition in SU(N) gauge theories
• Update of the Hagedorn mass spectrum
• Conformal Invariance and Degrees of Freedom in the QCD String
• Large Nc Continuum Reduction and the Thermodynamics of QCD
• Finite Temperature Gauge Theory from the Transverse Lattice

Cited by in corpus (10)

• Properties of hot and dense matter from relativistic heavy ion collisions
• Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups
• Hadron Mass Spectrum and the Shear Viscosity to Entropy Density Ratio of Hot Hadronic Matter
• Shear viscosity to entropy density ratio of a relativistic Hagedorn resonance gas
• QCD and the Hagedorn spectrum
• Does the empirical meson spectrum support the Hagedorn conjecture?
• Comments on Yang-Mills thermodynamics, the Hagedorn spectrum and the gluon gas
• The Hagedorn spectrum and large $N_c$ QCD in 2+1 and 3+1 dimensions
• Hadron resonance gas EoS and the fluidity of matter produced in HIC
• The thermodynamics of large-N QCD and the nature of metastable phases