Thermodynamics of two-dimensional QCD in the large-N limit.

Abstract

We study the thermodynamics of QCD in the limit of a large number of colors. It is argued that in this limit there is an order parameter for confinement, which is the energy density itself. We show that at a first-order confinement-deconfinement phase transition, the ratio of the latent heat of the phase transition to the energy density of matter in the hadronic phase is infinite. We explicitly study the 't Hooft model of two-dimensional QCD. It is shown that at any finite temperature the thermodynamic potential is not computable in perturbation theory, and that the high-temperature limit of the thermodynamic potential is infinite in the limit of zero interaction strength. We also demonstrate how the Feynman graphs for the thermodynamic potential may be resummed to produce the same contribution as that from a resonance gas of hadrons, and show that the thermodynamic potential which is nominally of order N is in fact of order 1. We argue that at an infinite temperature, T\ensuremath{\sim}(N\ensuremath{\sigma}${)}^{1/2}$, where \ensuremath{\sigma} is the string tension, the system may become a deconfined gas of quarks, but that there need be no phase transition at any finite temperature.