$p-$forms non-minimally coupled to gravity in Randall-Sundrum scenarios

TL;DR

This paper investigates how p-form fields non-minimally coupled to various geometrical tensors behave in Randall-Sundrum brane scenarios, analyzing localization, zero modes, and massive resonances, revealing conditions for their possible observation.

Contribution

It extends the analysis of p-form fields non-minimally coupled to geometrical tensors in Randall-Sundrum models, providing new conditions for zero mode localization and resonance behavior.

Findings

Zero modes can be localized under specific conditions.

Resonances are absent for vector fields but may appear in Ricci and Riemann couplings.

Massive unstable modes are more probable in Ricci and Riemann couplings.

Abstract

In this paper we study the coupling of $p$-form fields with geometrical tensor fields, namely Ricci, Einstein, Horndeski and Riemann in Randall-Sundrum scenarios with co-dimension one. We consider delta-like and branes generated by a kink and a domain wall. We begin by a detailed study of the Kalb-Ramond (KR) field. The analysis of KR field is very rich since it is a tensorial object and more complex non-minimal couplings are possible. The generalization to $p$-forms can provide more information about the properties and structures that can possibly be universal in the geometrical localization mechanism. The zero mode is treated separately and conditions for localization of zero modes of $p-$forms are found for all the cases above and with this we arrive at the above conclusion about vector fields. Another property that can be tested is the absence of resonances found in the case of vector fields. For this we analyze the possible unstable massive modes for all the above cases via transmission coefficient. Our conclusion is that we have more probability to observe massive unstable modes in the Ricci and Riemann coupling.