Eigenvalues of the Wilson operator in multicolor QCD

For continuum QCD with N = infinite we consider the spectral density rhosub(C)(α) of the eigenvalues α for the Wilson operator defined on the curve C. It is shown that a consequence of the Makeenko-Migdal equation rhosub(C)(α) satisfies a non-linear differential-integral equation. The equation for rhosub(C) is closely related to the condition for the occurrence of a saddle point in the functional integral when N = infinite. This interpretation is remarkably analogous to a result obtained by Gross and Witten for the two-dimensional Wilson lattice theory, although the equation satisfied by rhosub(C)(α) is much more complicated in the continuum theory. (orig.)