TY - JOUR

T1 - Some exact solutions of the semilocal Popov equations

AU - Kim, Chanju

N1 - Funding Information:
This work was supported by the Mid-career Researcher Program grant No. 2012-045385/2013-056327 and the WCU grant No. R32-10130 through NRF of Korea funded by the Korean government (MEST), and the Research fund No. 1-2008-2935-001-2 by Ewha Womans University .

PY - 2014/6/2

Y1 - 2014/6/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84900015517&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2014.05.001

DO - 10.1016/j.physletb.2014.05.001

M3 - Article

AN - SCOPUS:84900015517

SN - 0370-2693

VL - 733

SP - 253

EP - 257

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

ER -