Hierarchy in a double braneworld

Abstract

We show that the hierarchy between the Planck and the weak scales can follow from the tendency of gravitons and fermions to localize at different edges of a thick double wall embedded in an AdS 5 spacetime without reflection symmetry. This double wall is a stable BPS thick-wall solution with two subwalls located at its edges; fermions are coupled to the scalar field through Yukawa interactions, but the lack of reflection symmetry forces them to be localized in one of the subwalls. We show that the graviton zero-mode wave function is suppressed in the fermion edge by an exponential function of the distance between the subwalls, and that the massive modes decouple so that Newtonian gravity is recuperated.

Fermion localization on thick branes

“…On the other hand, dynamic walls with a cosmological de Sitter expansion are unable to localize even one chiral mode. We have considered here only the five dimensional version of the well-known solution of Goetz [14], but these results are expected to hold for other dynamic walls such as the ones found recently in [25]; work in this direction is now in progress [24].…”

“…A precise calculation of the tunneling probability for these massive left and right-handed modes is in order here, but will only make sense in a definite model in which the parameters of the potential can be related with the age of the Universe. This is beyond the scope of this paper and will be dealt with elsewhere [24]. It is however clear that the internal structure of the wall, i.e.…”

Localizing gauge fields on a topological Abelian string and the Coulomb law

“…Here we will assume the Nielsen Olesen anzats (6) as valid only to zero order, and look for the equations of the first order fluctuations but with the simplification given by (10). Moreover we will impose axial symmetry for all initial fields, sources and potential, that means that both gravity and electromagnetic fields must have axial symmetry.…”

“…Equation (44) is equivalent to (10). The 4 dimensional Maxwell field is considered to be a fluctuation from its null background value (6)…”

“…To do that, they introduce two different coupling constant for the electromagnetic field and very strict restrictions on the fields and parameters. Some recent calculations indicate very strict bounds on the wall thickness of many orders of magnitude thinner than the Planck scale [10] to achieve a 4 dimensional behavior. The loss of electromagnetic radiation at low frequency and the non preservation of charge are also drawbacks related to the confinement of gauge fields in domain wall brane worlds.…”