Induced QCD and Hidden Local ZN Symmetry

TL;DR

This paper analyzes a lattice QCD model with a $Z_N$ gauge symmetry, showing it exhibits confinement in the strong coupling phase and discussing the necessity of a phase transition for continuum QCD emergence.

Contribution

It demonstrates the presence of a $Z_N$ gauge symmetry in the induced lattice QCD model and discusses its implications for confinement and phase transitions.

Findings

The model exhibits local confinement with only color singlets propagating.

Wilson loops for non-singlets average to zero in the strong coupling phase.

A phase transition is likely necessary for the model to reach continuum QCD.

Abstract

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a $Z_N$ gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for non-singlets average to zero. We argue that, if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support presence of such a phase transition.