Confinement of Fermions via the Spin Connection

TL;DR

This paper explores how the degrees of freedom in the spin connection of Riemannian geometry can be utilized to confine fermions within a four-dimensional brane, offering a geometric mechanism for particle confinement.

Contribution

It introduces a novel approach to fermion confinement using the spin connection in Riemannian manifolds, expanding the geometric methods beyond non-Riemannian theories.

Findings

Spin connection degrees of freedom can trap fermions.

Fermion confinement achieved without non-Riemannian fields.

Potential implications for brane-world models.

Abstract

Recently there has been an interest in studying the role that geometry may play in the problem of confining fermions to our four-dimensional spacetime. In general, the focus is on non-Riemannian geometries which possess fields like torsion and non-metricity. In this paper, the degrees of freedom present in the spin connection in a Riemannian manifold are used to confine fermions. It turns out that one can use this connection to trap these particles inside a brane.