Localization of Bulk Matters on a Thick Anti-de Sitter Brane

TL;DR

This paper studies how gravity and various matter fields can be localized on a thick anti-de Sitter brane, analyzing their mass spectra and stability, and demonstrating localization of fermions with Yukawa coupling.

Contribution

It presents a detailed analysis of the localization and mass spectra of multiple bulk fields on a thick AdS brane, including gravity, scalars, vectors, and fermions, with stability considerations.

Findings

Gravity zero mode is not localized, but massive modes are trapped.

Thick AdS brane is stable under scalar perturbations.

Fermions are localized with Yukawa coupling, yielding chiral zero modes.

Abstract

In this paper, we investigate the localization and the mass spectra of gravity and various bulk matter fields on a thick anti-de Sitter (AdS) brane, by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schr\"{o}dinger equations. For gravity, the potential of the KK modes tends to infinity at the boundaries of the extra dimension, which leads to an infinite number of the bound KK modes. Although the gravity zero mode cannot be localized on the AdS brane, the massive modes are trapped on the brane. The scalar perturbations of the thick AdS brane have been analyzed, and the brane is stable under the scalar perturbations. For spin-0 scalar fields and spin-1 vector fields, the potentials of the KK modes also tend to infinity at the boundaries of the extra dimension, and the characteristic of the localization is the same as the case of gravity. For spin-1/2 fermions, by introducing the usual Yukawa coupling $\eta\bar{\Psi}\phi\Psi$ with the positive coupling constant $\eta$, the four-dimensional massless left-chiral fermion and massive Dirac fermions are obtained on the AdS thick brane.