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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- 1/N expansion
- Lattice gauge field theories
- Matrix models