Localization of Vector and Fermion Fields on a Thick Brane with a Lump-type Scalar Background

We study a thick braneworld model in asymptotically anti-de Sitter spacetime, supported by a non-topological lump-type scalar field. Unlike in boson stars, which are also non-topological solutions, the complex scalar field in our setup must have zero oscillation frequency. Consequently, the background scalar field is static and real, which breaks the global $U(1)$ symmetry. This is similar to spontaneous symmetry breaking, but it is not the same. We then investigate the localization of vector and fermion fields within this framework. By introducing a specific non-minimal coupling, we demonstrate that the zero modes of both fields can be successfully localized. Notably, this mechanism allows for the simultaneous localization of both left- and right-handed fermion zero modes.