Families of spinors in $d=(1+5)$ with zweibein and two kinds of spin connection fields on an almost $S^2$

TL;DR

This paper investigates the properties of spinor families in a six-dimensional model with curved extra dimensions, focusing on massless states and interactions with multiple spin connection fields within a Kaluza-Klein framework.

Contribution

It extends previous models by including multiple spin connection fields and analyzing the masslessness of spinor families in a curved extra-dimensional space.

Findings

Families of spinors form subgroups with even numbers of members.

Certain spinor states remain massless under specific spin connection configurations.

The model provides insights into spin-charge-family theory in higher dimensions.

Abstract

We studied (arxiv: 1001.4679, 1205.1714) properties of spinors in a toy model in $d=(1+5)$ as a step towards realistic Kaluza-Klein (like) theories in non compact spaces. ${\cal M}^{(5+1)}$ was assumed to break to an infinite disc with a zweibein which makes a disc curved on $S^2$ and with a spin connection field which allows on such a sphere only one massless spinor state. This time we are taking into account families of spinors interacting with several spin connection fields, as required for this toy model by the spin-charge-family theory We are studying possible masslesness of families of spinors: Spinors regroup into subgroups of an even number of families.