Thick brane solutions

Abstract

This article gives a comprehensive review on thick brane solutions and related topics. Such models have attracted much attention from many aspects since the birth of the brane world scenario. In many works, it has been usually assumed that a brane is an infinitely thin object; however in more general situations, one can no longer assume this. It is also widely considered that more fundamental theories such as string theory would have a minimal length scale. Many multidimensional field theories coupled to gravitation have exact solutions of gravitating topological defects, which can represent our brane world. The inclusion of brane thickness can realize a variety of possible brane world models. Given our understanding, the known solutions can be classified into topologically non-trivial solutions and trivial ones. The former class contains solutions of a single scalar (domain walls), multi-scalar, gauge-Higgs (vortices), Weyl gravity and so on. As an example of the latter class, we consider solutions of two interacting scalar fields. Approaches to obtain cosmological equations in the thick brane world are reviewed. Solutions with spatially extended branes (S-branes) and those with an extra time-like direction are also discussed.

Extended supersymmetry and BPS solutions in baby Skyrme models

“…The investigation of SUSY extensions of genuinely nonstandard kinetic terms has been resumed only recently [55]- [63] (see also [64]- [67] for related discussions), where this rising interest is partly owed to the fact that field theories with non-standard kinetic terms may be instrumental in the resolution of some enigmas of cosmology [68]- [80]. Concretely, in [56] we demonstrated that the baby Skyrme model in the O(3) formulation does have a N = 1 SUSY extension for arbitrary non-negative potential.…”

Supergravity-induced interactions on thick branes

“…First of all we fix the bulk dimension to five so that dimN = 5 for the notation we have introduced in the previous section. In this work we will consider the flat (Minkovski) geometry for the brane [28,29,54,55]. Therefore our 5D metric ansatz will be…”

“…These models fulfill the requirement of a fundamental length scale due to string theory. An updated review of these so-called thick branes can be found in [29] In [28] it is discussed that the localized interactions of bulk scalars on a thick brane solution of a warped 5D bulk can be described by a sigma-model in which the brane forming scalar is non-linearly coupled to the bulk scalar fields via its derivatives. In this manner the kinetic term of the brane forming scalar is a function of the bulk scalars.…”

Localization of abelian gauge fields on thick branes

“…Besides, such thin branes are static, with no dynamical mechanism responsible for their formation. In order to avoid the use of singular branes, thick branes modeled as domain wall configurations can be implemented in extra-dimensional theories (for a detailed review on thick brane solutions, see [3]). The key feature of this approach is that thick branes are dynamically generated by one or several background scalar fields coupled with gravity.…”