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Two-dimensional non-abelian quantum field models provide a useful laboratory for analytic and numerical investigations of quantum theories with gauge symmetry. They can exhibit various features, such as charge confinement, which are known from D=4 theories like QCD. Several analytic predictions concerning the spectra of two-dimensional systems with adjoint matter were postulated and numerical results were obtained using Discrete Light Cone Quantization techniques, however none of them has been checked via Monte Carlo simulations. In this Letter we present two such models which are particularly interesting from the physical point of view and discuss first numerical results.

Preliminary study of two-dimensional SU(N) Yang-Mills theory with adjoint matter with Hybrid Monte Carlo approach