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Fermion generations from “apple-shaped” extra dimensions. (English) Zbl 1326.81150
Summary: We examine the behavior of fermions in the presence of an internal compact 2-manifold which in one of the spherical angles exhibits a conical character with an obtuse angle. The extra manifold can be pictured as an apple-like surface, i.e., a sphere with an extra ‘wedge’ insert. Such a surface has conical singularities at north and south poles. It is shown that for this setup one can obtain, in four dimensions, three trapped massless fermion modes which differ from each other by having different values of angular momentum with respect to the internal 2-manifold. The extra angular momentum acts as the family label and these three massless modes are interpreted as the three generations of fundamental fermions.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
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