Entrapment of a network of domain walls

Abstract

We explore the idea of a network of defects to live inside a domain wall in models of three real scalar fields, engendering the Z2 × Z3 symmetry. The field that governs the Z2 symmetry generates a domain wall, and entraps the hexagonal network formed by the three-junctions of the model of two scalar fields that describes the remaining Z3 symmetry. If the host domain wall bends to the spherical form, in the thin wall approximation there may appear non-topological structures hosting networks that accept diverse patterns. If Z3 is also broken, the model may generate a buckyball containing sixty junctions, a fullerene-like structure. Applications to cosmology are outlined.PACS numbers: 11.27.+d, 11.30.Er, 98.80.Cq, 47.54.+r Domain walls appear in diverse branches of physics, as for instance in systems of condensed matter that present ferromagnetic [1], ferroelectric [2] and other properties [3], and also in cosmology [4,5]. They arise in systems with at least two isolated degenerate minima, and in field theory they usually live in three spatial dimensions as bidimensional objects, seen as immersions into (3, 1) dimensions of static solutions of (1, 1) dimensional models that engender the Z 2 symmetry. The standard domain wall presents no internal structure, but there are models where they may entrap field configurations that engender non-trivial behavior. This idea follows as in Refs. [6][7][8], and in the more recent Refs. [9,10]. Other investigations include for instance supersymmetry [11], supergravity [12], and the recent applications to polymers [13].Although domain walls may be dangerous [4,5] to cosmological applications, they have found their way into cosmology as for instance seeds for the formation of non-topological structures. This possibility appears in Refs. [14][15][16][17], where the discrete symmetry is changed to an approximate symmetry, or in Ref. [18], with the discrete symmetry biased so that domains of distinct but degenerate vacua spring unequally. The non-topological structures may be stable, but now stability requires the presence of conserved charges, of bosonic and/or fermionic origin.Domain walls may also be of interest when they host non-trivial structures. We illustrate this point using the model introduced in the first work of Ref.[10], describing the pair of fields (φ, χ) via the superpotential W (φ, χ) = −φ + (1/3)φ 3 + r φ χ 2 . Here r is a parameter, real and dimensionless, that couples the two fields. The system is described by a quartic potential, and we use natural units, working with dimensionless space and time variables, and fields. The equations of motion for field configurations φ = φ(z) and χ = χ(z) are solved by solutions of the first order differential equations dφ/dz = −1 + φ 2 + rχ 2 and dχ/dz = 2rφχ. In this model, the sector connecting the minima (±1, 0) is a BPS sector, with energy density or tension t = 4/3. For r > 0 this BPS sector admits two different types of static solutions: the one-field solutions φ 1 (z) = tanh(z) and χ 1 = 0, and the two-field solutions...

First-order formalism for twinlike models with several real scalar fields

“…[25][26][27][28][29]. We can also consider three-field models, as the ones used in [30][31][32], for instance; this would lead us to other twinlike models.…”

Deformed defects

“…[32,33]. Also, it may be of some use in more complex situations, involving three or more scalar fields, in scenarios such as the one where we deal with the entrapment of planar network of defects [34], or with the presence of non-trivial solutions representing orbits that connect vacuum states in the threedimensional configuration space [35].…”

Domain walls in three-field models

“…In Ref. [15] the idea of an hexagonal network of defect to be nested inside a topological defect has been investigated in a model described by three real scalar fields. That investigation has shown that when the host domain wall is driven to relax to cylindrical or spherical shape, the nested hexagonal network could give rise to structures resembling nanotubes or fulerenes, respectively.…”