Fermion Localization in an Extra‐Dimensional f(Q,T) Gravity With Cuscuton Dynamics

ABSTRACT

This paper is aimed at investigating a codimension‐one thick brane with cuscuton dynamics within the framework of modified symmetric teleparallel gravity, where is the nonmetricity scalar and is the energy‐momentum tensor trace. The brane is generated by a scalar field with noncanonical dynamics containing a cuscuton term, which modifies the structure of the scalar sector without introducing additional propagating degrees of freedom. By employing the first‐order formalism, analytical solutions for the scalar field, warp factor, scalar potential, and energy density are obtained for different choices of superpotentials, including sine‐Gordon, polynomial, and linear forms. We analyze how the parameters controlling the nonmetricity corrections and the matter coupling affect the internal structure and localization properties of the brane. In addition, the localization of spin‐ fermions is studied through a minimal Yukawa coupling between the fermionic field and the background scalar field. The resulting Schrödinger‐like equations exhibit a supersymmetric structure that guarantees the stability of the fermionic spectrum and allows the localization of the chiral zero mode on the brane. Furthermore, we investigate the spectrum of massive fermionic modes and identify resonant states through the relative probability method. The appearance of these quasi‐localized modes indicates the presence of metastable fermionic excitations associated with the internal structure of the brane.