Soliton models for thick branes

TL;DR

This paper introduces new soliton solutions for thick branes in 4+1 dimensions using scalar fields with broken symmetry, analyzing their stability, particle motion, and differences in stability among models.

Contribution

It presents novel thick brane models based on sine-Gordon, φ^4, and φ^6 scalar fields with broken symmetry, and studies their stability and particle dynamics.

Findings

φ^4 brane is stable

SG and φ^6 branes have unstable modes under certain conditions

Particle motion near the brane is characterized by geodesic equations

Abstract

In this work, we present new soliton solutions for thick branes in $4+1$ dimensions. In particular, we consider brane models based on the sine-Gordon ($SG$), $\varphi^{4}$ and $\varphi^{6}$ scalar fields, which have broken $Z_{2}$ symmetry in some cases, and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacuua. These vacuua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighbourhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the $w^2$ term in the expansion of the potential for the resulting Schrodinger-like equation, where $w$ is the 5-dimensional coordinate. It turns out that the $\varphi^4$ brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and $\varphi^6$ branes.