Evaluation of Observables in the Gaussian $N=\infty$ Kazakov-Migdal Model

TL;DR

This paper analyzes the behavior of observables, especially Wilson loops, in the Gaussian Kazakov-Migdal model at large N, providing explicit asymptotic formulas and discussing phase transitions.

Contribution

It offers explicit asymptotic formulas for observables in the Gaussian Kazakov-Migdal model and discusses phase transitions at large N.

Findings

Explicit formulas for adjoint Wilson loops asymptotics

Discussion of phase transition in the d=1 model

Analysis of N=infinity Itzykson-Zuber integrals

Abstract

We examine the properties of observables in the Kazakov-Migdal model. We present explicit formulae for the leading asymptotics of adjoint Wilson loops as well as some other observables for the model with a Gaussian potential. We discuss the phase transiton in the large $N$ limit of the $d=1$ model. One of appendices is devoted to discussion of the $N =\infty$ Itzykson-Zuber integrals for arbitrary eigenvalue densities.