Gauge theories of quark confinement in 2+1 dim: A comparative study of SU(2) Yang-Mills and Yang-Mills-Higgs systems

This chapter summarizes some recent work on the confinement problem in 2+1 dim. Reviews the Debye-Hueckel screening mechanism of confinement in the Yang-Mills-Higgs system due to Polyakov. Uses the Polyakov model and D'Hoker's Monte-Carlo results as a guide to construct the vacuum of the pure SU(2) gauge theory in terms of adjoint monopoles. The mechanism of quark confinement in the pure gauge theory is the one proposed by Wilson, Kogut and Susskind. Finds that a vacuum of adjoint monopoles does lead to a correct screening theory in the sense that only SU(2) representations with non-trivial Z2 charges are confirmed, unlike compact QED3 where all representations are confined. Concludes that using the presented preliminary ideas, it may be possible to prove confinement in this model and apply the same sort of idea for 3+1 dimensions