Localization of graviphoton and graviscalar on the brane

Abstract

The question of whether the Kaluza-Klein (KK) graviphoton $h_{5\mu}$ and graviscalar $h_{55}$ are localized or not on the brane is one of the important issues. In this letter, we address this problem in five dimensions. Here we consider the massless (zero-mode) propagations without requiring the Z$_2$-symmetry on $h_{5\mu}$. We obtain the graviton $h_{\mu\nu}$, graviphoton, and graviscalar exchange amplitudes on shell. We find that the graviscalar has a tachyonic mass. It turns out that $h_{5\mu}$ admits the localized zero-modes on the brane while $h_{55}$ does not have a localized zero-mode. This is contrasted to the fact that the bulk spin-0 field has a localized zero-mode on the brane but the bulk spin-1 field does not have a localized solution in five dimensions.