Thick brane solutions

TL;DR

This review comprehensively discusses thick brane solutions in higher-dimensional theories, highlighting their classifications, models, and cosmological implications, emphasizing the importance of finite brane thickness in brane world scenarios.

Contribution

It provides a systematic classification of thick brane solutions and reviews various models and approaches, including cosmological equations and extended brane configurations.

Findings

Classified solutions into topologically non-trivial and trivial types.

Reviewed models involving scalar fields, gauge-Higgs systems, and Weyl gravity.

Discussed solutions with spatially extended branes and extra time-like dimensions.

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.