A Gravity-Consistent Confinement of Fermions in Braneworld

TL;DR

This paper introduces a new covariant scalar-coupling mechanism for confining fermions on braneworlds, ensuring compatibility with gravity and allowing for localized massive modes, advancing the understanding of fermion confinement in higher-dimensional models.

Contribution

It proposes a novel covariant scalar-coupling function that facilitates fermion localization on braneworlds without altering the bulk metric, extending previous confinement mechanisms.

Findings

A covariant scalar-coupling function compatible with fermion confinement.

Existence of gravitational configurations with localized and discretized massive modes.

Confirmation that fermion zero-modes can be confined without modifying the bulk geometry.

Abstract

In this manuscript, we discuss the confinement of the spin $\frac{1}{2}$ field on a plethora of branewords models. Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), we studied the consistency of the Standard Model (SM) fields localization on braneworlds with the Einstein equation. In that paper, we discussed the consistency of the spinor field confinement and, by using a Yukawa-like interaction given by $\mathcal{L}_{int}\propto f(y)\bar{\Psi}\Psi$, we obtained that the function must be defined as $f(y)\propto e^{-A}A'$. This shape of the scalar function emerge from the requirement that the spin $\frac{1}{2}$ (zero-mode) localization cannot modify the metric on bulk. This ensures that the confinement of gravity on the brane is preserved. In the present manuscript, we find a covariant scalar-coupling function that can generate this interaction. This provide a new mechanism for localizing fermion fields over the brane. We also discuss massive modes and we found some gravitational configuration where there are confined and discretized massive modes.