An example of Kaluza-Klein-like theory with boundary conditions, which lead to massless and mass protected spinors chirally coupled to gauge fields

TL;DR

This paper proposes a Kaluza-Klein-like model with boundary conditions on a finite disk that enables the existence of massless, chiral spinors coupled to gauge fields, addressing a key challenge in higher-dimensional theories.

Contribution

It introduces a boundary condition approach in a 6D model that preserves massless, chiral spinors, overcoming previous difficulties in Kaluza-Klein theories.

Findings

Massless chiral spinors are achievable with boundary conditions.

Spinors of only one handedness are supported by the boundary.

Chiral coupling to gauge fields is successfully realized.

Abstract

The genuine Kaluza-Klein-like theories (with no fields in addition to gravity) have difficulties with the existence of massless spinors after the ompactification of some of dimensions of space\cite{witten}. We assume a $M^{(1+3)} \times$ a flat finite disk in $(1+5)$-dimensional space, with the boundary allowing spinors of only one handedness. Massless spinors then chirally couple to the corresponding background gauge gravitational field, which solves equations of motion for a free field, linear in the Riemann curvature.