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 $\bar{\mathrm{\Psi }}{\mathrm{\Gamma }}^M{\mathrm{\Gamma }}^N{\mathrm{\Gamma }}^P\cdots T_{MNP\cdots }\mathrm{\Psi }$, 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 $\bar{\mathrm{\Psi }}{\mathrm{\Gamma }}^M{\mathrm{\partial }}_{M}F(\phi ,R,R^{\mu \nu }{R}_{\mu \nu },\cdots )\mathrm{\Psi }$ may facilitate the localization of the spinor field when $F(\phi )={\phi }^n$.