The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory Original Research Article

Recently we have reported on the existence of finite energy SU(2) Yang–Mills–Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft–Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft–Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive image-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the image-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant image. However the dipole separation and the magnetic dipole moment decrease with image. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.