The Difference between Abelian and Non-Abelian Models: Fact and Fancy

Abstract

The commonly accepted belief that non-Abelian and Abelian models are different because of the presence/absence of instantons and/or perturbative asymptotic freedom is analyzed from a historical perspective. The presentation covers the major developments which brought about this dogma, as well as all the supportive evidence produced since. For a model possessing both asymptotic freedom and instantons it is shown rigorously that a disorder variable varies nonanalytically with the temperature.

20 pages, no figures. This paper reflects the state of affairs as it was in 1991. In some areas there have been important developments since then