"An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories

TL;DR

This paper explores a novel approach in Kaluza-Klein-like theories by utilizing effective two-dimensional cases, allowing for massless chiral spinor states without external gauge fields, potentially overcoming previous theoretical limitations.

Contribution

It introduces a method to achieve massless chiral spinors in higher-dimensional models through specific geometric configurations and spin connection choices, bypassing Witten's no-go theorem.

Findings

A single massless chiral spinor state is obtained on a curved disc

The approach does not require external gauge fields

The spectrum of spinor states is discrete and complete

Abstract

One step towards realistic Kaluza-Klein[like] theories and a loop hole through the Witten's "no-go theorem" is presented for cases which we call an effective two dimensionality cases: In $d=2$ the equations of motion following from the action with the linear curvature leave spin connections and zweibeins undetermined. We present the case of a spinor in $d=(1+5)$ compactified on a 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 normalizable spinor state of a particular charge, which couples the spinor chirally to the corresponding Kaluza-Klein gauge field. We assume no external gauge fields. The masslessness of a spinor is achieved by the choice of a spin connection field (which breaks parity), the zweibein and the normalizability condition for spinor states, which guarantee a discrete spectrum forming the complete basis. We discuss the meaning of the hole, which manifests the noncompactness of the space.