Generalized non-minimal couplings in Randall-Sundrum scenarios

TL;DR

This paper investigates how non-minimal geometrical couplings affect gauge field localization in Randall-Sundrum models, finding that certain couplings do not produce resonances and highlighting potential fundamental structures.

Contribution

It extends the localization mechanism by analyzing couplings with Ricci and Einstein tensors, revealing that divergenceless tensors do not localize zero modes and that these couplings do not generate resonances.

Findings

Localized zero mode exists with Ricci tensor coupling

No resonances are generated by geometrical couplings

Results are valid for various brane configurations and warp factors

Abstract

The Geometrical Localization mechanism in Randall-sundrum (RS) scenarios is extended by considering the coupling between a quadratic mass term and geometrical tensors. Since the quadratic term is symmetric, tensors with two symmetric indices have to be taken into account. These are the Ricci and the Einstein tensors. For the Ricci tensor it is shown that a localized zero mode exists while that is not possible for the Einstein tensor. It is already known that the Ricci scalar generates a localized solution but the metrics do not. Therefore, it can be conclude that divergenceless tensors do not localize the zero mode of gauge fields. The result is valid for any warp factor recovering the RS metrics at the boundaries, and therefore is valid for RS I and II models. We also compute resonances for all couplings. These are calculated using the transfer matrix method. The cases studied consider the standard RS with delta-like branes, and branes generated by kinks and domain-wall as well. The parameters are changed to control the thickness of the smooth brane. We find that, for all cases considered, geometrical coupling does not generate resonances. This enforces similar results for the coupling with the Ricci scalar and points to the existence of some unidentified fundamental structure of these couplings.