Universal Mass Scale for Bosonic Fields in Multi-Brane Worlds

TL;DR

This paper establishes a universal ultralight mass scale for all bosonic $p$-form fields in multi-brane models, introduces a covariant formulation, and explores their behavior in crystal-like backgrounds with implications for new physics at a common scale.

Contribution

It proposes a covariant approach to multi-localize $q$-form fields, revealing a universal ultralight mode with the same mass as gravity, and analyzes their behavior in crystal backgrounds with new band gap results.

Findings

All $q$-form fields have an ultralight mode with the same mass as gravity.

In crystal backgrounds, the wave functions are Bloch-like and exhibit band gap structures.

Dilaton coupling affects the mass of the first mode but cannot generate or suppress mass for $q$-forms.

Abstract

In this paper we find an universal mass scale for all $p-$forms in multi-brane worlds model. It is a known fact the this model provides an ultralight mode for the fields. However, to get this, the Lagrangians considered in the literature are not covariant. In order to solve this, we propose a covariant version to multi-localize $q-$form fields. As a consequence of the covariance, we show that all the $q$-form fields have an ultralight mode with the same mass that the gravitational one. That way we show that there is an universal mass scale for the ultralight modes of the bosonic fields. This suggests that a new physics must emerge, for all theses fields, at the same scale. After that, we revisit the results that consider a crystal manyfold background in the Randall-Sundrum scenary (RS), and add the discussion related to geometrical couplings in such a configuration. The wave functions of fields trapped in the crystal are Bloch-like waves, and their behavior is very similar to electrons inside a lattice, just like in the Kronig-Penney model (KP). We compute the mass dispersion relations for those fields with and without a dilaton coupling. It leads to new results for the band gap structure of these fields. In the case of the Kalb-Ramond field, and with the correct dispersion relation, there is no gap between the mass bands. Also, always that the field is coupled with the dilaton, its first mass mode decreases. When the generalization to the $q-$form is done, we show that it is not possible to suppress or generate mass for the fields by controlling the dilaton coupling, differently of what was argued previously.