Abstract
Polyakov loop eigenvalues and their $N$ dependence are studied in two- and four-dimensional $SU(N)$ Yang-Mills (YM) theory. The connected correlation function of the single-eigenvalue distributions of two separated Polyakov loops in two-dinemsional YM is calculated and is found to have a structure differing from the one of corresponding Hermitian random matrix ensembles. No large-$N$ nonanalyticities are found for two-point functions in the confining regime. Suggestions are made for situations in which large-$N$ phase transitions involving Polyakov loops might occur.
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