Massive $p$-form trapping as a $p$-form on a brane

TL;DR

This paper demonstrates a mechanism for trapping zero modes of p-form fields on branes, analyzes resonances, and provides analytical solutions in smooth scenarios, revealing unique features compared to previous models.

Contribution

It introduces a unified approach to trap zero modes of p-form fields on branes without splitting fields, and explores resonance phenomena with analytical solutions.

Findings

Zero modes can be trapped without splitting fields.

No resonances are observed in this trapping mechanism.

Analytical solutions are derived for specific smooth scenarios.

Abstract

It is shown here that the zero mode of any form field can be trapped to the brane using the model proposed by Ghoroku and Nakamura. We start proven that the equations of motion can be obtained without splitting the field in even and odd parts. The massive and tachyonic cases are studied revealing that this mechanism only traps the zero mode. The result is then generalized to thick branes. In this scenario, the use of a delta like interaction of the quadratic term is necessary leading to a "mixed" potential with singular and smooth contributions. It is also shown that all forms produces an effective theory in the brane without gauge fixing. The existence of resonances with the transfer matrix method is then discussed. With this we analyze the resonances and look for peaks indicating the existence of unstable modes. Curiously no resonances are found in opposition of other models in the literature. Finally we find analytical solutions for arbitrary $p-$forms when a specific kind of smooth scenario is considered.