We construct the first analytic examples of nonhomogeneous condensates in the Georgi-Glashow model at finite density in ($2+1$) dimensions. The nonhomogeneous 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 nonconstant 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 Lamé 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, is the one with the nonconstant 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.

• Received 18 August 2021
• Accepted 5 November 2021

DOI:https://doi.org/10.1103/PhysRevD.104.125002

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Published by the American Physical Society