Bosonic fields in crystal manifold

A crystal-like universe made of membranes in extra dimensions in a Randall–Sundrum scenario is studied. A background gravitational metric satisfying the right boundary conditions is considered to study the localization of the scalar, gauge and Kalb–Ramond fields. It is found that the wave function for the fields are Bloch waves. The mass modes equations are calculated allowing us to show the zero-gap mass behavior and the mass dispersion relation for each field. Finally we generalize all these results and consider q-forms in the crystal membrane universe. We add the dilaton interaction in order to guarantee localization of forms. We show that, due to the dimension D, the form q and the dilaton coupling λ, the mass spectrum can be the same for the different bosonic fields studied. Such a result is a different way to see the duality between forms