The Spectrum of the Kazakov Migdal-Model

TL;DR

This paper analyzes the spectrum of small fluctuations in the Kazakov-Migdal model, revealing a string-like spectrum that relates to mesons in lattice QCD and reproduces known matrix model results.

Contribution

It computes the fluctuation spectrum around Gross's semi-circular eigenvalue distribution, connecting it to string-like excitations and meson spectra in lattice QCD.

Findings

Identifies a string-like spectrum of fluctuations in the model.

Reproduces the known spectrum of the hermitean matrix model in one dimension.

Suggests relevance to extended objects in higher dimensions.

Abstract

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's 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 hermitean 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.