## Abstract

In 2+1 dimensional nonrelativistic Chern-Simons gauge theories on S^{2} which has a global SU(M) symmetry, the semilocal Popov vortex equations are obtained as Bogomolny equations by minimizing the energy in the presence of a uniform external magnetic field. We study the equations with many flavors and find several families of exact solutions. The equations are transformed to the semilocal Liouville equations for which some exact solutions are known. In this paper, we find new exact solutions of the semilocal Liouville equations. Using these solutions, we construct solutions to the semilocal Popov equations. The solutions are expressed in terms of one or more arbitrary rational functions on S^{2}. Some simple solutions reduce to CP^{M-1} lump configurations.

Original language | English |
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Pages (from-to) | 12-17 |

Number of pages | 6 |

Journal | Journal of the Korean Physical Society |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2014 |

## Keywords

- Chern-Simons theory
- Popov equation
- Semilocal
- Vortex