  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.
