Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
Abstract
We find the exact non-perturbative expression for a simple Wilson loop of arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription. The result differs from the standard pure exponential area-law of YM2, but still exhibits confinement as well as invariance under area-preserving diffeomorphisms and generalized axial gauge transformations. We show that the large N limit is NOT a good approximation to the model at finite N and conclude that Wu's N=infinity Bethe-Salpeter equation for QCD2 should have no bound state solutions. The main significance of our results derives from the importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional perturbative gauge theory.
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