Particles of One-Half Topological Charge

Details Particles of One-Half Topological Charge Particles of One-Half Topological Charge

2011-12-07

arxiv.org/abs/1112.1492v3

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 10 figures

Scientific paper

We would like to show the existence of finite energy SU(2) Yang-Mills-Higgs particles of one-half topological charge. The 't Hooft Abelian magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole located at the origin, $r=0$, and a semi-infinite Dirac string singularity located on one half of the z-axis which carries a magnetic flux of $\frac{2\pi}{g}$ going into the center of the sphere at infinity. Hence the net magnetic charge of the configuration is zero. The non-Abelian solutions possess gauge potentials that are singular at only one point, that is, on either the positive or the negative z-axis at large distances, elsewhere they are regular. There are two distinct different configurations of these particles with different total energies and energy distributions. The total energies of these one-half magnetic monopole solutions are calculated for various strength of the Higgs field self-coupling constant $\lambda$ and they are found to increase logarithmically with $\lambda$. These solutions do not satisfy the first order Bogomol'nyi equations and are non-BPS solutions.

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