Closed formula for Wilson loops for $SU(N)$ Quantum Yang-Mills Theory in two dimensions

Details Closed formula for Wilson loops for $SU(N)$ Quantum Yang-Mills Theory in two dimensions Closed formula for Wilson loops for $SU(N)$ Quantum Yang-Mills Theory in two dimensions

1996-05-18

arxiv.org/abs/hep-th/9605128v1

J.Math.Phys. 38 (1997) 5453-5482

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, Latex, no figures

Scientific paper

10.1063/1.532146

A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups $SU(N)$ and $U(1)$ and space-time topologies $\Rl^1\times\Rl^1$ and $\Rl^1\times S^1$. (For the $U(1)$ theory, we also consider the $S^1\times S^1$ topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied for the present model.

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