Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density

TL;DR

This paper presents the first analytic non-homogeneous condensate solutions in a 2+1 dimensional Yang-Mills-Higgs-Chern-Simons model at finite density, revealing topological stability and phase transitions depending on system size.

Contribution

It introduces novel analytic solutions for non-homogeneous condensates with topological charge in the 2+1D Georgi-Glashow model at finite density, including explicit magnetic flux and stability analysis.

Findings

Existence of non-homogeneous condensates with topological charge.

Reduction of field equations to Lamé equation for certain Higgs profiles.

Finite density phase transitions depending on system size.

Abstract

We construct the first analytic examples of non-homogeneous condensates in the Georgi-Glashow model at finite density in $(2+1)$ dimensions. The non-homogeneous condensates, which live within a cylinder of finite spatial volume, possess a novel topological charge that prevents them from decaying in the trivial vacuum. Also the non-Abelian magnetic flux can be computed explicitly. These solutions exist for constant and non-constant Higgs profile and, depending on the length of the cylinder, finite density transitions occur. In the case in which the Higgs profile is not constant, the full system of coupled field equations reduce to the Lam\'e equation for the gauge field (the Higgs field being an elliptic function). For large values of this length, the energetically favored configuration is the one with a constant Higgs profile, while, for small values, it is the one with non-constant Higgs profile. The non-Abelian Chern-Simons term can also be included without spoiling the integrability properties of these configurations. Finally, we study the stability of the solutions under a particular type of perturbations.