In 2+1 dimensional nonrelativistic Chern-Simons gauge theories on S2 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 S2. Some simple solutions reduce to CPM-1 lump configurations.
Bibliographical noteFunding Information:
This work was supported by a Mid-career Researcher Program grant (No. 2012-045385/2013-056327) and by a WCU grant (No. R32-10130) through NRF of Korea funded by the Korean government (MEST), and by the Research fund (No. 1-2008-2935-001-2) of Ewha Womans University.
- Chern-Simons theory
- Popov equation