https://doi.org/10.1140/epjc/s10052-026-16054-8
Regular Article - Theoretical Physics
Thick branes and fermion localization in five-dimensional 
gravity
1
Research Center for Quantum Physics, Huzhou Normal University, 313000, Huzhou, People’s Republic of China
2
Secretaria da Educação do Ceará (SEDUC), Coordenadoria Regional de Desenvolvimento da Educação (CREDE 9), 62880-384, Horizonte, Ceará, Brazil
3
Departamento de Física, Centro de Ciências Exatas e da Natureza, Universidade Federal da Paraíba, 58051-970, João Pessoa, Paraíba, Brazil
4
Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, 07700, Mexico City, CDMX, Mexico
5
National Observatory of Athens, Lofos Nymfon, 11852, Athens, Greece
6
CAS Key Laboratory for Researches in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and Technology of China, 230026, Hefei, Anhui, China
7
Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Avda. Angamos 0610, Antofagasta, Chile
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
21
April
2026
Accepted:
23
June
2026
Published online:
6
July
2026
Abstract
We investigate thick-brane configurations in five-dimensional modified teleparallel gravity. In five dimensions, the torsional Gauss–Bonnet invariant 
contributes dynamically, leading to genuinely new effects even at linear order. Within a warped geometry supported by a scalar field, we construct explicit solutions and show that the sector significantly modifies the brane structure. In particular, the coupling parameter controls the deformation of the warp factor and energy density; for sufficiently negative values it can induce a genuine two-peak internal structure. We further analyze the localization of spin-1/2 fermions via a Yukawa coupling. For odd Yukawa functions the system admits a normalizable chiral zero mode, while the opposite chirality remains delocalized. The massive Kaluza–Klein spectrum is strongly affected by the torsional Gauss–Bonnet term, which modifies the effective potentials and leads to the appearance of resonant quasi-localized states. Our results show that gravity provides a richer framework for braneworld models, where torsional higher-order corrections play a key role in shaping both geometry and field localization.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
