Above a critical area, a complex scalar on a torus with flux M develops a non-zero coordinate-dependent vacuum expectation value, yielding 1, 2, or 6 degenerate configurations for M=1,2,3 in the lowest-mode approximation.
Quark mass hierarchy and mixing via geometry of extra dimension with point interactions
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abstract
We propose a new model which can naturally explain origins of fermion generations, quark mass hierarchy, and Cabibbo-Kobayashi-Maskawa matrix simultaneously from geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermion at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of non-diagonal elements of fermion mass matrices is found to be severely restricted due to geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy.
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A 6D SO(16) GUT model unifies SM gauge groups with SU(3) family symmetry by placing three chiral generations into one spinor representation, canceling anomalies via vectorlike 6D fermions and fixed-point localized states while noting asymptotic freedom of the SO(16) coupling.
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Vacuum structure of a scalar field on a torus with uniform magnetic flux
Above a critical area, a complex scalar on a torus with flux M develops a non-zero coordinate-dependent vacuum expectation value, yielding 1, 2, or 6 degenerate configurations for M=1,2,3 in the lowest-mode approximation.
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Family Unification in $SO(16)$ Grand Unification
A 6D SO(16) GUT model unifies SM gauge groups with SU(3) family symmetry by placing three chiral generations into one spinor representation, canceling anomalies via vectorlike 6D fermions and fixed-point localized states while noting asymptotic freedom of the SO(16) coupling.