A dynamical symmetry breaking model in Weyl space

TL;DR

This paper investigates the process of dynamical symmetry breaking from Weyl to Riemannian geometry by analyzing the motion of de Sitter bubbles modeled as thin shells within a Weyl-Dirac framework, revealing how scalar fields connect interior and exterior geometries.

Contribution

It introduces a novel thin shell solution in Weyl-Dirac theory to model symmetry breaking and explores how scalar fields mediate geometric transitions.

Findings

Exact spherically symmetric solutions for de Sitter bubbles

Scalar field beta links interior and exterior geometries

Potential applications in geometric symmetry breaking

Abstract

The dynamical process following the breaking of Weyl geometry to Riemannian geometry is considered by studying the motion of de Sitter bubbles in a Weyl vacuum. The bubbles are given in terms of an exact, spherically symmetric thin shell solution to the Einstein equations in a Weyl-Dirac theory with a time-dependent scalar field of the form beta = f(t)/r. The dynamical solutions obtained lead to a number of possible applications. An important feature of the thin shell model is the manner in which beta provides a connection between the interior and exterior geometries since information about the exterior geometry is contained in the boundary conditions for beta.