Eigenvalue density of Wilson loops in 2DSU(N) YM

Abstract

In 1981 Durhuus and Olesen (DO) showed that at infinite N the eigenvalue density of a Wilson loop matrix W associated with a simple loop in two-dimensional Euclidean SU(N ) Yang-Mills theory undergoes a phase transition at a critical size. The averages of det(z − W ), det(z − W ) −1 , and det(1 + uW )/(1 − vW ) at finite N lead to three different smoothed out expressions, all tending to the DO singular result at infinite N . These smooth extensions are obtained and compared to each other.

k-string tensions and the1/Nexpansion

“…10 Transformation properties under N ! ÀN were also considered by Lohmeyer, Neuberger, and Wettig [34] in connection with their study of the density of eigenvalues of Wilson loops in two dimensions. Although the context is quite different, some of their expressions are in form reminiscent of relationships that we derive here.…”

Nonanalyticity in Scale in the Planar Limit of QCD

“…The approximate validity of a "diffusive" viewpoint (that is, using the HK as a model) for the behavior of Wilson loops has been pointed out already in 2005 [8], for the case of the gauge group SU(2). The exact formula for the single eigenvalue-angle density in the HK case at any N was derived in [9]. Casimir dominance has been discussed at the perturbative level in [10] and at the nonperturbative one it was reviewed by Greensite in [11].…”

From loops to surfaces

“…The case D = 2 is exactly soluble so the universal form is known [5]. This phase transition is seen only in Q(z, C ), but not in the individual W k 's and is therefore different from the familiar Gross-Witten phase transition [6].…”