# Massless fermions localization on domain walls

## TL;DR

This paper studies how massless fermions can be localized on scalar domain walls in a 5D Anti de-Sitter spacetime, revealing a normalizable state influenced by Yukawa interactions and gravitational effects.

## Contribution

It demonstrates the existence of a normalizable fermion state on domain walls, independent of $Z_2$ symmetry, due to the interplay of Yukawa coupling and gravity.

## Key findings

- Normalizable fermion state identified on domain walls.
- Fermion migration toward the wall edge due to Yukawa-gravity competition.
- Localization effect independent of $Z_2$ symmetry.

## Abstract

Massless fermions on scalar domain walls are considered. Two walls are established, corresponding to 5-dimensional static spacetime asymptotically Anti de-Sitter, differentiated by the symmetry around the wall, and in each case massless chiral fermions are coupled to the wall by a Yukawa term. We identify a normalizable state associated to the migration of fermions toward the edge of the wall. This effect is generated by the competition between the Yukawa interaction and the gravitational repulsion on the matter fields, and it is independent of the $Z_2$ symmetry of the wall.