The Problem of Large-N Phase Transition in Kazakov-Migdal Model of Induced QCD

TL;DR

This paper investigates the Kazakov-Migdal lattice gauge model for inducing QCD, focusing on the large-N phase transition and its implications for continuum QCD, using a mean field approach to analyze phase transition behavior.

Contribution

It introduces a detailed analysis of the large-N phase transition in the Kazakov-Migdal model and proposes a mean field framework applicable to arbitrary potentials.

Findings

No first order phase transition occurs for quadratic potential

The large-N phase transition precedes the continuum limit transition

Discussion of the model's symmetry and observable construction

Abstract

We study the lattice gauge model proposed recently by Kazakov and Migdal for inducing QCD. We discuss an extra local Z_N which is a symmetry of the model and propose of how to construct observables. We discuss the role of the large-N phase transition which should occur before the one associated with the continuum limit in order that the model describes continuum QCD. We formulate the mean field approach to study the large-N phase transition for an arbitrary potential and show that no first order phase transition occurs for the quadratic potential.