Two-dimensional Yang-Mills theory: A model of quark confinement

We analyze the structure of two-dimensional Yang-Mills theory as a model of quark confinement. 't Hooft's solution, in the large-$N$ limit, is extended to investigate the consistency and the properties of the model. We construct the hadronic color singlet bound-state scattering amplitudes. We show that they are unitary, that colored states cannot be produced, and that all long-range interactions are absent. Current amplitudes are constructed, and we show that the theory is asymptotically free and the quark mass sets the scale of mass corrections. The properties of bound states of heavy quarks are discussed, and a dynamical basis for the Okubo-Zweig-Iizuka rule is suggested. We show how confinement can occur with an infrared prescription that leads to finite-mass quarks which decouple from physical states and discuss the dependence of gauge-variant amplitudes on the cutoff procedure. Higher-order effects in $\frac{1}{N}$ are shown not to change the qualitative features of the model.