Brane World as a Result of Spontaneous Symmetry Breaking

TL;DR

This paper explores how brane worlds can naturally emerge from spontaneous symmetry breaking as topological defects, analyzing their gravitational properties and potential implications for dark matter and hierarchy problems.

Contribution

It provides a self-consistent macroscopic theory of brane worlds from phase transitions, comparing approaches with vector and multiplet order parameters, and identifies solutions with brane features.

Findings

Regular solutions with brane-like properties are found.

Brane configurations can trap matter and generate mass differentiation.

Potential solutions address dark matter and hierarchy issues.

Abstract

The theories of brane world and multidimensional gravity are widely discussed in the literature in connection with problems of evolution of early Universe, including dark matter and energy. A natural physical concept is that a distinguished surface in the space-time manifold is a topological defect appeared as a result of a phase transition with spontaneous symmetry breaking. The macroscopic theory of phase transitions allows considering the brane world concept self-consistently, even without the knowledge of the nature of physical vacuum. Gravitational properties of topological defects (cosmic strings, monopoles,...) in extra dimensions are studied in General Relativity considering the order parameter as a vector and a multiplet in a plane target space of scalar fields. The common results and differences of these two approaches are analyzed and demonstrated in detail. Among the variety of regular solutions, there are those having brane features, including solutions with multiple branes, as well as the ones of potential interest from the standpoint of the dark matter and hierarchy problems. Regular configurations have a growing gravitational potential and are able to trap the matter on the brane. If the energy of spontaneous symmetry breaking is high, the attracting potential can have several points of minimum. Identical in the uniform bulk spin-less particles, being trapped within the separate points of minimum, acquire different masses and appear to an observer on brane as different particles with integer spins.