5d Dirac fermion on quantum graph

Abstract

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.

Instantons and Berry's connections on quantum graph

“…This imply that the eigenvalues of U are ±1 and therefore, U is given by a Hermitian unitary matrix. This boundary condition corresponds to the one discussed in the previous paper [15] and leads to the same structure of eigenfunctions. We can then classify the boundary condition and zero mode solutions in accordance with the previous paper.…”

“…This is because that the structure of the supersymmetric quantum mechanics is hidden in this CT invariant system as well as in Ref. [15]. In this system, the "Hamiltonian" H , the supercharge Q and the "fermion number" operator (−1) F in the supersymmetric quantum mechanics can be given as H = Q 2 , Q = H D , (−1) F = σ 3 .…”

“…(For reviews of quantum graph, see [1,2].) This system has been applied to various research areas such as scattering theory, nanotechnology on one dimensional graphs [3][4][5][6], quantum chaos [7][8][9], supersymmetric quantum mechanics [10][11][12], extra dimensional models [13][14][15] and so on, due to fascinating structures from boundary conditions. Therefore, the study of boundary conditions on the quantum graph will contribute to the further development of low and high energy physics.…”

“…In this paper, we investigate non-Abelian Berry's connections in a parameter space of boundary conditions of quantum graphs to reveal further nontrivial configurations. In the previous paper [15], we have considered a 1+4 dimensional (1+4d) Dirac fermion on quantum graphs and classified the degeneracy of Dirac zero modes. This study will also be applicable to a fermion on quantum graphs in various dimensions.…”

Large Star/Rose Extra Dimension with Small Leaves/Petals

“…That is why we choose in this work the more straigtforward approach of Refs. [36,53] where a 5D field is defined on the whole metric graph from the start.…”