Fermion localization on degenerate and critical branes

TL;DR

This paper investigates how fermions can be localized on degenerate and critical Bloch branes by analyzing the interaction coupling constants directly in physical coordinates, providing new insights especially for degenerate branes.

Contribution

It introduces a new analysis of fermion localization on degenerate Bloch branes and proposes a coupling mechanism for localizing massless fermions on both sides of a double-brane.

Findings

Fermion zero-modes can be localized with specific coupling constants.

Results for critical branes agree with previous studies.

New results for degenerate Bloch branes are presented.

Abstract

In this work we analyze the localization of fermions on degenerate and critical Bloch branes. This is done directly on physical coordinates, in constrast to some works that has been using conformal coordinates. We find the range of coupling constants of the interaction of fermions with the scalar fields that allow us to have normalizable fermion zero-mode localized on the brane on both, critical and degenerate Bloch branes. In the case of critical branes our results agree with those found in [Class. Quantum Grav. \textbf{27} (2010) 185001]. The results on fermion localization on degenerate Bloch branes are new. We also propose a coupling of fermions to the scalar fields which leads to localization of massless fermion on both sides of a double-brane.