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An example of Kaluza-Klein- like theory with boundary conditions, which lead to massless and mass protected spinors chirally coupled to gauge fields
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
a flat finite disk in -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.Comment: 10 pages, references adde