The coexistence of a ’t Hooft-Polyakov monopole and a one-half monopole

Abstract

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 −12 while the magnetic charge of the ’t Hooft-Polyakov monopole is positive unity. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z-axis that carries the magnetic monopole charge of another −12. The solution possesses gauge potentials that are singular along the z-axis, elsewhere they are regular. This monopole configuration possesses finite total energy and magnetic dipole moment. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ. However the dipole separation and the magnetic dipole moment decrease with λ. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.