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2009

Eigenvalue density of Wilson loops in 2D SU(N) YM

Lohmayer, Robert, Neuberger, Herbert, Wettig, Tilo

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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), 1/det(z-W), 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.

Eigenvalue density of Wilson loops in 2D SU(N) YM · Around

Built on

A. M. Perelomov and V. M. Popov, Casimir operators for the unitary group
1965
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Dover, 1978
H. S. Wilf, Mathematics for the Physical Sciences · 1978
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B. Durhuus and P. Olesen, The spectral density for two-dimensional continuum QCD
1981
Earlier work this paper cites.
G. V. Dunne, Negative dimensional groups in quantum physics
1989
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Academic Press, San Diego, 2nd ed., 1991
M. L. Mehta, Random Matrices · 1991
Earlier work this paper cites.
American Mathematical Society, Providence, RI, 1991
G. Szegö, Orthogonal Polynomials · 1991
Earlier work this paper cites.

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