Localisation of Fermions to brane: Codimension $d \geq 2$

TL;DR

This paper explores how fermions can be localized on branes in higher-dimensional models, showing that localization depends on the fermion type and background configurations, with successful localization for isospinor fermions in various topological backgrounds.

Contribution

It demonstrates that fermion localization on branes in higher dimensions is achievable for isospinor fermions using specific topological backgrounds, expanding understanding of fermion confinement mechanisms.

Findings

Localization is power-law in instanton backgrounds.

Localization is exponential in soliton backgrounds.

Fermion localization fails for isoscalar fermions.

Abstract

We investigate $4+d$ dimensional fermionic models in which the system in codimension-$d$ supports a topologically stable solution, and in which the fermion may be localised to the brane, with power law in 'instanton' backgrounds and exponentially in 'soliton' backgrounds. When the fermions are isoscalars, the mechanism fails, while for isospinor fermions it is successful. As backgrounds we consider instantons of Yang--Mills and sigma models in even codimensions, solitons of sigma models in odd codimensions, as well as solitons of Higgs and Goldstone models in all codimensions.