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

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.