Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on $f(T,B)$-thick brane

TL;DR

This paper explores how torsion and boundary terms in $f(T,B)$ gravity influence the localization of gauge and Kalb-Ramond fields on thick branes, introducing a Stueckelberg-like coupling to achieve zero mode confinement and analyzing the spectrum for resonances.

Contribution

It introduces a novel geometrical coupling mechanism in $f(T,B)$ gravity to localize gauge fields on thick branes, using first-order formalism with sine-Gordon and $ ext{phi}^4$ potentials.

Findings

Successful localization of zero modes for gauge and Kalb-Ramond fields.

Identification of resonant massive modes without tachyonic instabilities.

Demonstration of a consistent thick brane setup with non-minimal couplings.

Abstract

In the context of $f(T,B)$ modified teleparallel gravity, we investigate the influence of torsion scalar $T$ and boundary term $B$ on the confinement of both the gauge vector and Kalb-Ramond fields. Both fields require a suitable coupling in five-dimensional braneworld scenarios to yield a normalizable zero mode. We propose a Stueckelberg-like geometrical coupling that non-minimally couples the fields to the torsion scalar and boundary term. To set up our braneworld models, we use the first-order formalism in which two kinds of superpotential are taken: sine-Gordon and $\phi^{4}$-deformed. The geometrical coupling is used to produce a localized zero mode. Moreover, we analyze the massive spectrum for both fields and obtain possible resonant massive modes. Furthermore, we do not find tachyonic modes leading to a consistent thick brane.