Lack of thermalization in (1+1)-d QCD at large $N_c$

Motivated by recent works aimed at understanding the status of equilibration and the eigenstate thermalization hypothesis in theories with confinement, we return to the 't Hooft model, the large-$N_c$ limit of (1+1)-d quantum chromodynamics. This limit has been studied extensively since its inception in the mid-1970s, with various exact results being known, such as the quark and meson propagators, the quark-antiquark interaction vertex, and the meson decay amplitude. We then argue this model is an ideal laboratory to study non-equilibrium phenomena, since it is manifestly non-integrable, yet one retains a high level of analytic control through large-$N_c$ diagrammatics. We first elucidate what are the non-equilibrium manifestations of the phenomenon of large-$N_c$ volume independence. We then find that within the confined phase, there is a class of initial states that lead to a violation of the eigenstate thermalization hypothesis, i.e. the system never thermalizes. This is due to the existence of heavy mesons with an extensive amount of energy, a phenomenon that has been numerically observed recently in the quantum Ising chain.