The 't Hooft model as a testing ground for Quantum Chromodynamics

Abstract: We study a 1+1 dimensional Yang-Mills model in the light-cone gauge (the ’t Hooft model). The colour group is SU (N ) and we study the limit N → ∞, the limit is taken such that g²N is kept constant. In this limit the only contributing diagrams are planar diagrams without gluon-gluon interactions. Using this, it is shown that there are no free quarks in this model. The bound state wave equation is derived which gives the meson masses and light-cone momentum space wave functions for the model. From this the decay amplitudes are calculated and we show that the model is not integrable and that the pion (massless meson) decouples. We also calculate the form factors which qualitatively show the charge distribution inside the meson.