Are the Dirac particles of the Standard Model dynamically confined states in a higher-dimensional flat space?

TL;DR

This paper explores a higher-dimensional model where Dirac particles are confined by a harmonic oscillator potential, potentially explaining particle generations and allowing escape at high energies, extending previous soliton confinement ideas.

Contribution

It extends the Dirac equation to eight dimensions with a harmonic oscillator potential, proposing a new confinement mechanism that resembles Standard Model particles and suggests a finite number of generations.

Findings

Bound states form in SU(4) x SU(2) representations.

Potential limits the number of particle generations.

Particles can escape at high energies, propagating freely in higher dimensions.

Abstract

Some time ago Rubakov and Shaposhnikov (RS) suggested that elementary particles might be excitations trapped on a soliton in a flat higher dimensional space. They gave as an example phi-4 theory in five dimensions with a bosonic excitation on a domain wall in the fifth dimension. They also trapped a chiral Dirac particle on the domain wall. We extend the RS field equation for the Dirac particle to eight flat dimensions (M4 X R4) and replace the one-dimensional domain-wall potential with a harmonic- oscillator "potential" in the four higher dimensions. This generates bound states in approximate SU(4) X SU(2) representations. These representations have corresponding "orbital" times "spin" quantum numbers and bear some resemblance to the quarks and leptons of the Standard Model. Soliton-theory suggests that the harmonic-oscillator potential should rise only a finite amount. This will then limit the number of generations in a natural way. It will also mean that particles with sufficient energy might escape the well altogether and propagate freely in the higher dimensions. It may be worth- while to search for a soliton (instanton?) which can confine Dirac particles in the manner of the harmonic-oscillator potential.