Harmonic maps, SU (N) skyrme models and yang-mills theories

Abstract

This thesis examines the construction of static solutions of (3+l)-dimensional SU{N) Skyrme models, usual and alternative, and pure massive SU(N) Yang-Mills theories. In particular, the application of harmonic maps from S(^2) into the subspace of fields configuration space M. Here, the harmonic maps are used as an ansatz to factoring out the angular dependence part of the solutions from the field equations. In this thesis, we consider the harmonic maps S(^2) → Gr(n, N), where Gr(n, N) is the Grassmann manifold of n-dimensional planes passing through the origin in C(^N). Using the harmonic map ansatz of S(^2) → Gr(2, N) to study the usual SU(N) Skyrme models, we have found that our approximate solutions have marginally higher energies in comparison to the corresponding results previously obtained using CP(^N-1) as target space M. For exact spherically symmetric solutions, we present arguments which suggest that the only solutions obtained this way are embeddings. For the alternative SU(N) Skyrme models, using the harmonic map ansatz of S(^2) → CP(^N-1), we have found that our results for the energies of the exact spherically symmetric solutions are higher than in the usual models. When considering the pure massive SU(N) Yang-Mills theories, we have shown that by choosing the gauge potential to be of almost pure gauge form, the theories reduce to the usual SU(N) Skyrme models. This observation has suggested to us to consider the harmonic map ansatz of S(^2) → CP(^N-1) previously applied to monopole theories. Using this ansatz, we have constructed some bounded spherically symmetric solutions of the theories having finite energies. [brace not closed]