5d Dirac fermion on quantum graph

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 (2N + 1) 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.