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Construction of topological defect networks with complex scalar fields.pdf

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Construction of topological defect networks with complex scalar fields

a r X i v : 0 8 0 5 .1 0 8 6 v 3 [ h e p - t h ] 1 8 S e p 2 0 0 8 Construction of topological defect networks with complex scalar fields V.I. Afonsoa, D. Bazeiaa, M.A. Gonzalez Leo?nb, L. Losanoa, and J. Mateos Guilartec aDepartamento de Fisica, Universidade Federal da Para??ba, BRAZIL bDepartamento de Matematica Aplicada, Universidad de Salamanca, SPAIN cDepartamento de Fisica and IUFFyM, Universidad de Salamanca, SPAIN This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build networks of topological defects, which appear from complex field models with potentials that engender a finite number of isolated minima, both in the case where the minima present discrete symmetry, and in the non symmetric case. We show that the presence of symmetry guide us to the construction of regular networks, while the non symmetric case gives rise to irregular networks which spread throughout the complex field space. We also discuss bifurcation, a phenomenon that appear in the non symmetric case, but is washed out by the deformation procedure used in the present work. PACS numbers: 11.10.Lm, 11.27.+d I. INTRODUCTION Defect structures have appeared in high energy physics almost fifty years ago, with some of the pioneer results collected in Refs. [1, 2, 3, 4]. Along the years, the subject has grown in importance, accompanied with an increasing number of investigations on kinks in one spatial dimension, vortices in two dimensions and monopoles in three dimensions, among other topological defects – see, e.g. [5] for an extensive discussion of some of the most important results in the area. The classical solutions which represent the defect structures can be of topological or non topological nature, and here we will deal with perhaps the simplest topological structures, which appear in models of scalar fiel