O modelo de Skyrme-Faddeev para SU(N)

Abstract

In this work we made a study about integrable systems in dimensions greater than two, specially the Skyrme-Faddeev model. We also proposed a submodel for the SU(N) Syrme-Faddeev model. The model is idealized by Skyrme [19] to SU(2) has in its Lagrangian derivate terms with order greater than two. These new terms are important to have stable static soliton like solutions in (3+1) dimensions. Faddeev [8] generalized the Skyrme idea to models in the sphere and shown the existence of solitons with topological charge given by the Hopf number, i.e π3 (S2). More recently, Faddeev and Niemo [11] conjectured that the Skyrme-Faddeev model could descrive the infrared limit of the Yang-Mills theory for the SU(N) without matter. The Hopf solitons could be interpreted as the glueballs. We found the equations of motion of the Skyme-Faddeev model in thems of the zero curvature condition. A study of the model to SU(3) was made and generalized to SU(N). A parametrization of SU(3) in therms of the complex fields v1, v2, v3 was made and the zero curvature potential was then written as function of the complexfields. Finally, we wrote the zero curvature condition in a generical SU(3) representation in order to verify the relevant constraints that lead to an integravel submodel.