The Spatial Dynamics in Kazakov--Migdal Model

TL;DR

This paper investigates the spatially inhomogeneous large N solutions of the Kazakov--Migdal model, deriving nonlinear differential equations and exploring their interpretations and stability issues across different dimensions.

Contribution

It derives continuum limit equations for the model and analyzes their interpretation and stability, highlighting differences between one-dimensional and multidimensional cases.

Findings

One-dimensional equations relate to Fermi gas dynamics.

Multidimensional solutions are unstable due to eigenvalue collapse.

Inconsistencies arise in higher dimensions because of instability.

Abstract

The spatially inhomogeneous large $N$ solutions to Kazakov--Migdal model are analyzed. The set of nonlinear differential equations is derived in the continuum limit. In one dimensional case these equations has a natural interpretation in terms of the dynamics of a Fermi gas. The multidimensional case seems to be inconsistent because of its instability related to the collapse of eigenvalues of the scalar field.