Deformed defects

Abstract

We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically expressed in terms of the defects of the original theory. The method is general, valid for both topological and non-topological defects, and we show how it extends to quantum mechanics, and how it works when the scalar field couples to fermions. We illustrate the general procedure with several examples, which support kink-like or lump-like defects. PACS numbers: 11.27.+d, 11.30.Er, 11.30.Pb Defects play important role in modern developments of several branches of physics. They may have topological or non-topological profile, and in Field Theory the topological defects usually appear in models that support spontaneous symmetry breaking, with the best known examples being kinks and domain walls, vortices and strings, and monopoles [1]. Domain walls, for example, are used to describe phenomena having rather distinct energy scales, as in high energy physics [1,2] and in condensed matter [3].The defects that we investigate in this letter are topological or kink-like defects, and nontopological or lumplike defects. They appear in models involving a single real scalar field, and are characterized by their amplitude and width, the width being related to the region in space where the defect solution appreciably deviates from vacuum states of the system. Interesting models that support kink-like defects involve polynomial potentials like the φ 4 model, periodic potentials like the sineGordon model, and even the vacuumless potential recently considered in [4,5]. We shall investigate defects by examining their solutions and the corresponding energy densities, to provide quantitative profile for both topological and nontopological defects.We introduce a general procedure to create deformed defects, starting from a known solvable model in one spatial dimension. We start with topological defects, and we show below that the proposed scheme generates, for each given model having topological solutions, infinitely many new solvable models possessing deformed topological defects. We examine stability of kink-like defects, to extend the procedure to quantum mechanics. We also investigate lump-like defects, to generalize the procedure to both topological and non-topological defects. Finally, we couple the scalar field to fermions, to show how the procedure works for the Yukawa coupling.The interest in kink-like defects is directly related to the role of symmetry restoration in cosmology [1,2] and in condensed matter [3]. Also, they are particularly important in other scenarios, where they may induce interesting effects. A significant example concerns the behavior of fermions in the background of kink-like structures [6]. The main point here is that symmetry breaking induces an effective mass term for fermions. In the background of the kink-like structure the fermionic mass varies from negative to...

Kink interactions in the(1+1)-dimensionalφ6model

“…On the other hand, the case of (1+1) dimensions can be more easily investigated, hence the use of (1+1)-dimensional systems as simplified models. Note that it is an actively developing area, with many important results obtained recently: the topological defect deformation procedure [4,5], the construction of a topological defect carrying U(1) charge in a system with two scalar fields -one real and one complex [6,7], Q balls in scalar theories with U(1) symmetry [8,9], and many others. There are interesting results in scalar systems with an interaction with a spinor field [10][11][12].…”

Spinors fields in co-dimension one braneworlds

“…The deformation method is based in modifications of the potential of models containing solitons in order to produce new and unexpected solutions [32]. Now we introduce the deformation parameter, called s, that controls the kind of deforming topological defect, in order to simulate different classes of branes.…”

Classical behavior of deformed sine-Gordon models

“…The deformation method, introduced in Ref. [42] and extended in Refs. [43,44,45], consists in the following general prescription.…”

“…II, where we review some basic facts on the deformation procedure first introduced in [42] and further explored in Refs. [43,44,45,46,47,48,49].…”