An example of Kaluza-Klein-like theories leading after compactification to massless spinors coupled to a gauge field

TL;DR

This paper demonstrates that in certain Kaluza-Klein-like theories, massless, chiral spinors can exist after compactification on a flat torus with suitable boundary conditions, addressing a key challenge in such models.

Contribution

It provides an explicit example showing the existence of massless, chiral spinors coupled to gauge fields in a compactified Kaluza-Klein framework, overcoming previous difficulties.

Findings

Massless spinors can exist after compactification with appropriate boundary conditions.

Massless solutions are protected and chirally coupled to gauge fields.

The example uses a flat torus as the compactified space.

Abstract

The genuine Kaluza-Klein-like theories (with no fields in addition to gravity with torsion) have difficulties with the existence of massless spinors after the compactification of some of dimensions of space\cite{witten}. We demonstrate in this letter on an example of a flat torus - as a compactified part of an (1+5)-dimensional space - that for constant fields and appropriate boundary conditions there exists in the 1+3 dimensional space a massless solution, which is mass protected and chirally coupled with a Kaluza-Klein charge to the corresponding gauge field.