Perturbative stability of non-Abelian electric field solutions

TL;DR

This paper investigates the stability of non-Abelian electric field solutions in SU(2) gauge theory with a scalar field, identifying stable regions and instabilities related to scalar mass parameters.

Contribution

It provides the first detailed analysis of perturbative stability for these non-Abelian electric solutions, highlighting conditions for stability and instability.

Findings

Stable solutions exist in certain parameter regions.

Instability occurs in one branch when scalar mass squared is negative.

Two solution branches are identified with different stability properties.

Abstract

We consider SU(2) gauge theory with a scalar field in the fundamental representation. The model is known to contain electric field solutions sourced by the scalar field that are distinct from embedded Maxwell electric fields. We examine the perturbative stability of the solution and identify a region of parameter space where the solution is stable. In the regime where the scalar field has a negative mass squared, the solution has two branches and we identify an instability in one of the branches.