Localization mechanism of $q-$form field on the brane-world by coupling with gravity

Abstract: It is known that the scalar fields can be trapped on branes of different types, and the $U(1)$ gauge vector fields can be localized on the thick de Sitter brane, or the thick Minkowski brane via coupling with gravity. The Kalb-Ramond fields can be localized on the Minkowski brane and the thick de-Sitter brane, with certain couplings. In this paper, with considering a coupling mechanism between the kinetic term of the $q-$form fields and the background spacetime, we investigate the localization of Kaluza-Klein modes for the $q-$form fields in $D-$dimensional spacetime. Concrete $q-$form fields are discussed within five-dimensional brane models with typical spacetime geometries: Minkowski, de Sitter, and Anti-de Sitter. In the Minkowski brane case, the zero modes of various $q-$form fields can be localized on the brane. In the de Sitter brane case, the zero mode of the $U(1)$ gauge vector fields can be localized on the brane. Lastly in the Anti-de Sitter brane case, the zero mode of the Kalb-Ramond fields can be localized on the brane. For the massive Kaluza-Klein modes of these $q-$form fields, they could be localized or quasi-localized on the brane of different types. Besides, subtle and detailed behaviors of the Kaluza-Klein modes for $q-$form fields are observed: the zero modes could be localized on both sides of the brane, and the massive modes could be localized or quasi-localized at the brane position.