Universality of large N phase transitions in Wilson loop operators in two and three dimensions

Abstract

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N. We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with the Wilson loop operator in two dimensional QCD. We hypothesize that the transition in three and four dimensional large N QCD are also in the same universality class and provide a numerical test for our hypothesis in three dimensions.

43 pages, 1 table, 18 figures, uses JHEP3.cls, one reference added, replaced Figure 3 and a small change to eqn (4.8)