Spontaneous Symmetry Breaking in General Relativity. Vector Order Parameter

TL;DR

This paper explores how a vector order parameter causes spontaneous symmetry breaking in a higher-dimensional gravitational setting, leading to regular solutions that can trap matter and produce particle mass differentiation.

Contribution

It introduces a novel approach using a vector order parameter in gravity, contrasting previous scalar multiplet methods, and analyzes the resulting solutions both analytically and numerically.

Findings

Existence of regular solutions with a negative cosmological constant.

Gravitational potential with multiple minima trapping particles.

Particles acquire different masses based on minima, mimicking particle diversity.

Abstract

Gravitational properties of a hedge-hog type topological defect in two extra dimensions are considered in General Relativity employing a vector as the order parameter. All previous considerations were done using the order parameter in the form of a multiplet in a target space of scalar fields. The difference of these two approaches is analyzed and demonstrated in detail. Regular solutions of the Einstein equations are studied analytically and numerically. It is shown that the existence of a negative cosmological constant is sufficient for the spontaneous symmetry breaking of the initially plain bulk. 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 gravitational potential has several points of minimum. Identical in the uniform bulk spin-less particles, being trapped within separate minima, acquire different masses and appear to the observer on brane as different particles with integer spins.