Calculation of Wilson loops in 2-dimensional Yang-Mills theories

Details Calculation of Wilson loops in 2-dimensional Yang-Mills theories Calculation of Wilson loops in 2-dimensional Yang-Mills theories

1999-01-28

arxiv.org/abs/hep-th/9901155v1

Annals Phys. 283 (2000) 11-56

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, Latex, 5 figures included (psfig, epsfig)

Scientific paper

10.1006/aphy.2000.6044

The vacuum expectation value of the Wilson loop functional in pure Yang-Mills theory on an arbitrary two-dimensional orientable manifold is studied. We consider the calculation of this quantity for the abelian theory in the continuum case and for the arbitrary gauge group and arbitrary lattice action in the lattice case. A classification of topological sectors of the theory and the related classification of the principal fibre bundles over two-dimensional surfaces are given in terms of a cohomology group. The contribution of SU(2)-invariant connections to the vacuum expectation value of the Wilson loop variable is also analyzed and is shown to be similar to the contribution of monopoles.

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