Spinor states on a curved infinite disc with non-zero spin-connection fields

TL;DR

This paper extends previous work on spinor states in a curved infinite disc by analyzing both massless and massive solutions across the entire parameter range of the spin connection field, highlighting conditions for a single massless state.

Contribution

It provides a comprehensive analysis of spinor solutions on a curved infinite disc with variable spin connection fields, generalizing prior specific cases.

Findings

Massless and massive spinor states are characterized for all parameter ranges.

Only one massless solution exists within the specified parameter space.

The results support the viability of chiral spinor coupling in higher-dimensional models.

Abstract

In the paper of Lukman, Mankoc Borstnik, Nielsen (NJP 13 (2011) 103027) one step towards the realistic Kaluza-Klein[like] theories was made by presenting the case of a spinor in $d=(1+5)$ compactified on an (formally) infinite disc with the zweibein which makes a disc curved on an almost $S^2$ and with the spin connection field which allows on such a sphere only one massless spinor state of a particular charge, coupling the spinor chirally to the corresponding Kaluza-Klein gauge field. The solutions for the massless spinor state were found for a range of spin connection fields, as well as the massive ones for a particular choice of the spin connection field. In this paper we present the massless and massive spinor states for the whole range of parameters of the spin connection field, which allow only one massless solution.