Localization of Spinor Fields in Higher-Dimensional Braneworlds

This study investigates the localization of spinor fields in braneworld models in six or higher dimensions. We study the relationship between fermions in spacetimes of $2n+2$ and $2n$ dimensions. In conformally flat extra-dimensional spacetime, fermions cannot be localized through minimal coupling with gravity. To achieve the localization of spinor fields, we introduce a tensor coupling term given by $\bar{\Psi} \Gamma^{M}\Gamma^{N}\Gamma^{P}\cdots T_{MNP\cdots} \Psi$, which ensures $SO(n, 1)$ symmetry. For a tensor $T_{MNP\cdots}$ of odd order, the left and right chiralities of high-dimensional spinors are decoupled. We find that a special form of tensor coupling $\bar{\Psi}\Gamma^{M} \partial_M {F(\phi, R, R^{\mu\nu}R_{\mu\nu},\cdots)} \Psi$ may facilitate the localization of the spinor field when $F(\phi) = \phi^n$.