It has recently been shown that a certain model field theory [which gives the Abelian Higgs model a global SU(2) symmetry by duplicating the scalar sector] possesses static finite-energy vortex solutions despite having a simply connected vacuum manifold. It is demonstrated here that they are stable or unstable according to whether ${\mathit{m}}_{\mathit{s}}$ is less than or greater than ${\mathit{m}}_{\mathit{v}}$ (where ${\mathit{m}}_{\mathit{s}}$ and ${\mathit{m}}_{\mathit{v}}$ are the masses of the Higgs and vector particles, respectively). At the boundary, ${\mathit{m}}_{\mathit{s}}$=${\mathit{m}}_{\mathit{v}}$, there is a two-parameter family of solutions all saturating a Bogomol’nyi bound. The relationship of the vortices to ${\mathrm{CP}}^{\mathit{n}}$ σ-model lumps is pointed out.

• Received 24 September 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.1263