Localization of Bulk Matters on a Thick Anti-de Sitter Brane
  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. 
Yu-Xiao Liu, Heng Guo, Chun-E Fu, Hai-Tao Li
hep-th gr-qc hep-ph