Localization of Matters on Anti-de Sitter Thick Branes

Abstract

By presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, we investigate the localization and mass spectra of various bulk matter fields on an AdS thick brane. For a spin 0 scalar $Φ$ coupled with itself and the domain-wall-forming field $ϕ$ via a coupling potential $V=(λϕ^{2}-u^{2})Φ^{2}+τΦ^{4}$, the localization and spectrum are decided by a critical coupling constant $λ_{0}$. When $λ>λ_0$, the potential of the scalar KK modes in the corresponding Schrödinger equation tends to infinite when far away from the brane, which results in that there exist infinite discrete scalar bound KK states, and the massless modes could be trapped on the AdS brane by fine-tuning of parameters. When $λ<λ_0$, the potential of the scalar KK modes tends to negative infinite when far away from the brane, hence there does not exist any scalar bound KK state. For a spin 1 vector, the situation is same like the scalar with a coupling constant $λ>λ_0$, but the zero mode can not be localized on the brane. For a spin 1/2 fermion, we introduce the usual Yukawa coupling $η\barΨϕΨ$, and find that the localization of the fermion is decided by a critical coupling constant $η_0$. For $η> η_0$, the four-dimensional massless left chiral fermion and massive Dirac fermions consisted of the pairs of coupled left-hand and right-hand KK modes could be localized on the AdS brane, and the massive Dirac fermions have a set of discrete mass spectrum. While for the case $0<η< η_{0}$, no four-dimensional Dirac fermion can be localized on the AdS brane.