Are two-dimensional Yang-Mills gauge theories "color" dependent?

If the symmetry of the theory under global transformations generated by the charges is normal, the physical states of the system must be "color" singlets. (This is analogous to the physical states of two-dimensional quantum electrodynamics being neutral.) Consequently, the local color currents vanish in physical states. The (two-dimensional) inhomogeneous Lorentz invariance of the theory is also discussed.