Thick brane solitons breaking $Z_2$ symmetry

TL;DR

This paper introduces new thick brane soliton solutions in 4+1 dimensions using scalar fields like sine-Gordon, , and , highlighting cases where $Z_2$ symmetry is broken and analyzing particle motion near the branes.

Contribution

It presents novel thick brane solutions with broken $Z_2$ symmetry based on specific scalar field potentials, and studies their stability and particle dynamics.

Findings

Broken $Z_2$ symmetry due to non-degenerate vacuua.

Scalar field potentials support and stabilize thick branes.

Geodesic analysis reveals particle behavior near branes.

Abstract

New soliton solutions for thick branes in 4 + 1 dimensions are considered in this article. In particular, brane models based on the sine-Gordon (SG), $\varphi^{4}$ and $\varphi^{6}$ scalar fields are investigated; in some cases $Z_{2}$ symmetry is broken. Besides, these soliton solutions are responsible for supporting and stabilizing the thick branes. In these models, the origin of the symmetry breaking resides in the fact that the modified scalar field potential may have non-degenerate vacuua and these non-degenerate vacuua determine the cosmological constant on both sides of the brane. At last, in order to explore the particle motion in the neighborhood of the brane, the geodesic equations along the fifth dimension are studied.