Non-axisymmetric baby-skyrmion branes

TL;DR

This paper explores non-axisymmetric solutions in a 6D gravitating baby-Skyrme brane model, revealing deformations at higher topological charges that could address the fermion mass hierarchy problem.

Contribution

It generalizes non-symmetric baby-Skyrme brane solutions to include gravity and extra dimensions, for higher topological charges, using numerical methods.

Findings

Non-axisymmetric solutions exist for higher topological charges.

Deformations may help explain fermion mass hierarchy.

Solutions are obtained via successive over relaxation method.

Abstract

We investigate the existence of non axisymmetric solutions in the 6-dimensional baby-Skyrme brane model. The brane is described by a localized solution to the baby-Skyrme model extending in the extra dimensions. Such non symmetric branes have already been constructed in the original 2+1-dimensional baby-Skyrme model in flat space. We generalize this result to the case of gravitating baby-Skyrme and in the context of extradimensions. These non-trivial deformation from the axisymmetric shape appear for higher values of the topological charge, so we consider the cases of $B=3,4$, where $B$ is the topological charge. We solve the coupled system of the Einstein and baby-Skyrme equations by successive over relaxation method. We argue that the result may be a possible resolution for the fermion mass hierarchy puzzle.