Some exact solutions of the semilocal Popov equations

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We study the semilocal version of Popov's vortex equations on S2. Though they are not integrable, we construct two families of exact solutions which are expressed in terms of rational functions on S2. One family is a trivial embedding of Liouville-type solutions of the Popov equations obtained by Manton, where the vortex number is an even integer. The other family of solutions is constructed through a field redefinition which relates the semilocal Popov equation to the original Popov equation but with the ratio of radii 3/2, which is not integrable. These solutions have vortex number N = 3n - 2 where n is a positive integer, and hence N = 1 solutions belong to this family. In particular, we show that the N = 1 solution with reflection symmetry is the well-known CP1 lump configuration with unit size where the scalars lie on S3 with radius 3/2. It generates the uniform magnetic field of a Dirac monopole with unit magnetic charge on S2.

Original languageEnglish
Pages (from-to)253-257
Number of pages5
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
StatePublished - 2 Jun 2014


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