# Fermionic bound states in distinct kinklike backgrounds

## TL;DR

This paper studies how geometric deformations in localized kink-like structures affect fermionic bound states in two-dimensional spacetime, comparing different backgrounds and interactions to understand their influence on physical properties.

## Contribution

It introduces an analysis of fermionic bound states in various kink-like backgrounds with geometric deformations, considering supersymmetric and Yukawa interactions.

## Key findings

- Geometric deformations alter fermionic bound state properties
- Different backgrounds lead to distinct fermion localization patterns
- Supersymmetric and Yukawa couplings produce varied bound state spectra

## Abstract

This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and consider two distinct boson-fermion interactions, one motivated by supersymmetry and the other described by the standard Yukawa coupling.