THE SPECTRUM OF THE KAZAKOV-MIGDAL MODEL

Gross has found an exact expression for the density of eigenvalues in the simplest version of the Kazakov-Migdal model of induced QCD. In this paper we compute the spectrum of small fluctuations around Gross' semi-circular solution. By solving Migdal's wave equation we find a string-like spectrum which, in four dimensions, corresponds to the infinite tower of mesons in strong coupling lattice QCD with adjoint matter. In one dimension our formula reproduces correctly the well-known spectrum of the hermitian matrix model with a harmonic oscillator potential. We comment on the relevance of our results to the possibility of the model describing extended objects in more than one dimension.