Non-integrability of Self-dual Yang-Mills-Higgs System

TL;DR

This paper investigates the integrability of the self-dual Yang-Mills-Higgs system in the Higgs phase, focusing on vortex and domain wall equations, and finds they lack the Painleve property, indicating non-integrability.

Contribution

It demonstrates that vortex and domain wall equations in the self-dual Yang-Mills-Higgs system are not integrable by analyzing their Painleve property.

Findings

Vortex equations do not have Painleve property.

Domain-wall equations do not have Painleve property.

These equations are not integrable.

Abstract

We examine integrability of self-dual Yang-Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painleve property. This fact suggests that these equations are not integrable.