Compactification with U(1) magnetic field within Dirac supersymmetry

TL;DR

This paper explores how a U(1) magnetic field within Dirac supersymmetry can induce compactification and mass generation, offering an alternative to traditional Kaluza-Klein theories by analyzing spectral properties across different dimensions.

Contribution

It demonstrates that a U(1) magnetic field can produce compactification-like behavior and mass creation in Dirac equations, providing new insights into dimensional reduction mechanisms.

Findings

Magnetic field induces compactification behavior in Dirac systems.

Explicit spectra are obtained for 6D to 4D and 4D to 2D reductions.

A dynamical mass-creation mechanism is proposed.

Abstract

We consider Dirac-supersymmetric interactions, which produce CP-conserving separation of positive and negative energy solutions in the Dirac equation in order to investigate an alternative to the Kaluza-Klein mechanism. We review conditions under which separation is possible into free particle and compactified behaviors in different dimensions, with attention to spin degrees of freedom. We show a U(1) constant magnetic field produces such kind of behavior; an explicit treatment is given to the 6-d to 4-d and 4-d to 2-d breaking cases and the spectrum is obtained. A dynamical mass-creation mechanism is suggested from the procedure.