New mechanism for fermion localization in $f(T,T_G)$-brane

TL;DR

This paper explores how modifications in teleparallel gravity, specifically through the $f(T,T_G)$ function, influence fermion localization and resonance phenomena in a five-dimensional braneworld model.

Contribution

It introduces a new mechanism showing how torsional modifications affect fermionic zero modes, resonances, and information distribution in braneworld scenarios.

Findings

Only one chiral fermion component can be localized on the brane.

Resonant states appear due to the internal structure of the effective potentials.

Torsional modifications lead to stronger localization and information redistribution.

Abstract

We investigate the localization of fermionic fields in a five-dimensional braneworld scenario within the framework of modified teleparallel gravity described by a general $f(T,T_G)$ function. Considering a non-minimal coupling between a Dirac spinor and the torsional invariants, we derive the effective Schr\"odinger-like equations governing the Kaluza-Klein modes. We showed that the contribution of the teleparallel Gauss-Bonnet term significantly modifies the effective potentials and, consequently, the localization properties. The zero-mode analysis reveals that only one chiral component can be localized on the brane, with the degree of confinement depending on the chosen model. In the massive sector, the spectrum is continuous, but resonant states arise due to the internal structure of the potentials. Additionally, we employ information-theoretic measures, such as Shannon entropy and relative probability, to quantify the localization mechanism. Our results show that the torsional modifications induce a nontrivial redistribution of information, exhibiting stronger localization. These findings highlight the role of higher-order torsional terms in shaping fermionic localization and resonance structures in braneworld scenarios.