On monopoles in low energy string theory and non-abelian particle trajectories

Abstract

This thesis is mainly concerned with monopoles. First, the existence of monopoles and their behaviour in the Yang-Mills-Higgs theories, and in parallel, the instanton solutions of the Yang-Mills fields are explained. One part of this work is about monopoles and instantons in low-energy string theory. A general instanton solution for the heterotic string theory is obtained by using the ADHM construction for the classical subgroups of the string gauge group. In this direction, the embedding of subgroups and a general formula for the dilaton are explained. In the next topic of this part, the i/-monopole and its generalisation to different subgroups of the string gauge group are discussed. In the second part, the motion of the Yang-Mills particles in the Yang-Mills- Higgs fields are studied. Planar orbits are observed for a particle in a monopole field when the Higgs field contribution is neglected. The planar orbits are studied further with some numerical analysis of the equations of motion. By regarding the Higgs field contribution, a complete set of equations are worked out for the particle and fields. In this scenario, the planar motions as well as three-dimensional bounded motions are studied. At the end, the force exerted by the non-abelian Yang-Mills-Higgs fields on a particle with non-abelian charge is explored.