Thick branes via higher order field theory models with exponential and power-law tails

TL;DR

This paper constructs exact thick brane models in five dimensions using higher order scalar field theories with $ ext{phi}^{10}$ and $ ext{phi}^{18}$ potentials, analyzing their stability, symmetry, and tail behaviors.

Contribution

It introduces new thick brane solutions with exponential and power-law tails from higher order field theories, including stability analysis and symmetry properties.

Findings

Two $ ext{phi}^{10}$ models are stable.

Branes with exponential tails lack $Z_2$-symmetry.

Some models exhibit unstable modes depending on parameters.

Abstract

In this work, we obtain exact thick brane models in $4+1$ dimensions generated by higher order field theory kinks, inspired by specific potentials for $\phi^{10}$ and $\phi^{18}$ models. We verify that the geodesic equation along the fifth dimension confirms the confining effects of the scalar field on the brane for all of these models. These models provide new solutions with exponential and power-law tails which live in different topological sectors. We show that the resulting branes of specific exponential law models do not possess $Z_2$-symmetry. 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 Schr\"{o}dinger-like equation. It turns out that two of the three models of the $\phi^{10}$ brane are stable, while another contains unstable modes for certain ranges of the model parameters. We also show that the brane solution from the specific $\phi^{18}$ models are stable, while the others involve neutral equilibrium. The asymptotic behaviour of the brane solutions are also discussed.