In this work we investigate the role of the symmetry of the Lagrangian on the existence of defects in systems of coupled scalar fields. We focus attention mainly on solutions where defects may nest defects. When space is non-compact we find topological BPS and non-BPS solutions that present internal structure. When space is compact the solutions are nontopological sphalerons, which may be nested inside the topological defects. We address the question of classical stability of these topological and nontopological solutions and investigate how the thermal corrections may modify the classical scenario.

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...

In this paper we analyze the local localization of gravity in AdS 4 thick brane embedded in AdS 5 space. The 3-brane is modelled by domain wall solution of a theory with a bulk scalar field coupled to five-dimensional gravity. In addition to small four-dimensional cosmological constant, the vacuum expectation value (vev) of the scalar field controls the emergence of a localized four-dimensional quasi-zero mode. We introduce high temperature effects, and we show that gravity localization on a thick 3-brane is favored below a critical temperature T c . These investigations suggest the appearance of another critical temperature T * , where the thick 3-brane engenders the geometric AdS/M/dS transitions.

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