Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription

TL;DR

This paper derives an exact non-perturbative expression for Wilson loops in two-dimensional Yang-Mills theory using the Wu-Mandelstam-Leibbrandt prescription, revealing differences from standard results and implications for large N limits.

Contribution

It provides the first exact non-perturbative Wilson loop expression in 2D YM with Wu-Mandelstam-Leibblst prescription, highlighting finite N effects and the absence of bound states at large N.

Findings

Exact Wilson loop expression differs from standard area-law

Large N limit does not approximate finite N behavior

No bound states at large N in the model

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 YM_2, 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 QCD_2 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.