Localization of spinor fields in higher-dimensional braneworlds

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 Ψ¯ΓMΓNΓP⋯TMNP⋯Ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\Psi}{\Gamma}^M{\Gamma}^N{\Gamma}^P\cdots {T}_{MNP\cdots}\Psi $$\end{document}, which ensures SO(n, 1) symmetry. For a tensor TMNP⋯ of odd order, the left and right chiralities of high-dimensional spinors are decoupled. We find that a special form of tensor coupling Ψ¯ΓM∂MFϕRRμνRμν⋯Ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\Psi}{\Gamma}^M{\partial}_MF\left(\phi, R,{R}^{\mu \nu}{R}_{\mu \nu},\cdots \right)\Psi $$\end{document} may facilitate the localization of the spinor field when F(ϕ) = ϕn.