A Study of the $N=2$ Kazakov-Migdal Model

TL;DR

This paper investigates the SU(2) Kazakov-Migdal model by numerically simulating gauge fields without integrating them out, revealing phase transition behavior, symmetry properties, and implications for the model's continuum limit.

Contribution

It provides new numerical insights into the phase structure and symmetries of the SU(2) Kazakov-Migdal model with gauge fields retained in simulations.

Findings

Confirmed a line of first order phase transitions ending at a critical point.

Observed a discontinuity in the adjoint plaquette across the transition.

Identified extra local U(1) symmetries affecting the continuum limit.

Abstract

We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In contrast to our earlier work on the subject we have chosen here {\it not} to integrate out the gauge fields but to keep them in the Monte Carlo simulation. This allows us to measure observables associated with the gauge fields and thereby address the problem of the local $Z_2$ symmetry present in the model. We confirm our previous result that the model has a line of first order phase transitions terminating in a critical point. The adjoint plaquette has a clear discontinuity across the phase transition, whereas the plaquette in the fundamental representation is always zero in accordance with Elitzur's theorem. The density of small $Z_2$ monopoles shows very little variation and is always large. We also find that the model has extra local U(1) symmetries which do not exist in the case of the standard adjoint theory. As a result, we are able to show that two of the angles parameterizing the gauge field completely decouple from the theory and the continuum limit defined around the critical point can therefore not be `QCD'.