Localization of spinor fields in higher-dimensional braneworlds

Abstract

In this paper we investigate the localization of spinor fields in braneworld models by reducing a Dirac spinor in 2n + 2-dimensional spacetime to spinors in 2n dimensions. The high-dimensional Dirac can be reduced to low-dimensional spinors including Weyl or Dirac. 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 $\overline{\mathrm{\Psi }}{\mathrm{\Gamma }}^M{\mathrm{\Gamma }}^N{\mathrm{\Gamma }}^P\cdots T_{\mathit{MNP}\cdots }\mathrm{\Psi }$, which ensures SO(n, 1) symmetry. For a tensor T_MNP⋯ of odd order, the left and right chiralities of high-dimensional spinors are decoupled. We find that a special form of tensor coupling $\overline{\mathrm{\Psi }}{\mathrm{\Gamma }}^M{\partial }_{M}F\left(\varphi ,R,R^{\mathit{\mu \nu }}{R}_{\mathit{\mu \nu }},\cdots \right)\mathrm{\Psi }$ may facilitate the localization of the spinor field when F(ϕ) = ϕⁿ.