Large-N Quenching in the Kazakov-Migdal Model

TL;DR

This paper investigates the large-N behavior of the Kazakov-Migdal model using a quenched momentum approach, revealing a quartic action dependence and suggesting phase transitions in certain dimensions.

Contribution

It introduces an approximation method for analyzing the Kazakov-Migdal model at large N, highlighting a shift from quadratic to quartic action dependence and indicating possible phase transitions.

Findings

Quartic dependence of the action on unitary matrices at large N.

Approximate analysis suggests phase transitions for dimensions less than 4 and 8.

Critical coupling values are identified for these phase transitions.

Abstract

To study the behavior of the Kazakov-Migdal at large N the quenched momentum prescription with constraints for treating the large N limit of gauge theories is used. It is noted that it leads to a quartic dependence of an action on unitary matrix instead of a quadratic dependence discussed in previous considerations. Therefore the model is not exactly solvable in the weak coupling limit. An approximation procedure for investigation of the model is outlined. In this approximation an indication to a phase transition for $d<4,8$ with $\beta_{cr}=\frac{1}{d-4,8}$ is obtained.