# Fermion Localization and Degenerate Resonances on Brane Array

## TL;DR

This paper explores how fermions can be localized and form resonant states on multi-wall braneworlds generated by scalar fields, revealing a novel degeneracy phenomenon in resonant states for multiple walls.

## Contribution

It constructs two analytic multi-wall solutions and uncovers the emergence of doubly-degenerate fermion resonant states in multi-wall configurations.

## Key findings

- Massless fermion is the only bound state.
- Resonant states are non-degenerate for one and two walls.
- Doubly-degenerate resonant states appear for three and four walls.

## Abstract

In this work, we consider the multi-wall braneworld arisen from multi-scalar fields, and investigate the localization and resonances of spin-1/2 fermion on the multi-walls. We build two analytic multi-wall solutions with a polynomial superpotential and a modified sine-Gordon superpotential respectively. The massless fermion is the only bound state and localized between the two outermost sub-branes. The factors affecting the number of massive resonant fermions are analyzed. What interesting is that all the fermion resonant states are non-degenerate for the cases of single- and two-walls, however, doubly-degenerate fermion resonant states emerge for the cases of three- and four-walls. This novel phenomenon could be potentially interesting in phenomenology.