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The thermodynamics of large-N QCD and the nature of metastable phases

In the limit of a large number of colors (N), both Yang-Mills and quantum chromodynamics are expected to have a first-order phase transition separating a confined hadronic phase and a deconfined plasma phase. One aspect of this separation is that at large N, one can unambiguously identify a plasma regime that is strongly coupled. The existence of a first-order transition suggests that the hadronic phase can be superheated and the plasma phase supercooled. The supercooled deconfined plasma present at large N, if it exists, has the remarkable property that it has negative absolute pressure -- i.e. a pressure below that of the vacuum. For energy densities of order unity in a 1/N expansion but beyond the endpoint of the hadronic superheated phase, a description of homogeneous matter composed of ordinary hadrons with masses of order unity in a 1/N expansion can exist, and acts as though it has a temperature of $T_H$ in order unity. However, the connection between the canonical and microcanonical descriptions breaks down and the system cannot fully equilibrate as $N \rightarrow \infty$. Rather, in a hadronic description, energy is pushed to hadrons with masses that are arbitrarily large. The thermodynamic limit of large volumes becomes subtle for such systems: the energy density is no longer intensive. These conclusions follow provided that standard large N scaling rules hold, the system at large N undergoes a generic first-order phase transition between the hadronic and plasma phases and that the mesons and glueballs follow a Hagedorn-type spectrum.