In this paper, we investigate a five-dimensional Dirac fermion on a quantum graph that consists of a single vertex and N loops. We find that the model possesses a rich structure of boundary conditions for wavefunctions on the quantum graph and they can be classified into distinct categories. It is then shown that there appear degenerate four-dimensional chiral massless fermions in the four-dimensional mass spectrum. We briefly discuss how our model could naturally solve the problems of the fermion generation, the fermion mass hierarchy and the origin of the CP-violating phase.
In this paper, we study non-Abelian Berry’s connections in the parameter space of boundary conditions for Dirac zero modes on quantum graphs. We apply the ADHM construction, which is the method for constructing Yang–Mills instanton solutions, to the Berry’s connections. Then we find that the instanton configurations appear as the Berry’s connections.
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