# 5d Dirac fermion on quantum graph

## TL;DR

This paper explores a five-dimensional Dirac fermion on a quantum graph with multiple loops, revealing a complex boundary condition structure and the emergence of chiral massless fermions, potentially addressing fundamental fermion physics issues.

## Contribution

It introduces a novel quantum graph model with a rich boundary condition classification and demonstrates the natural appearance of chiral fermions in four dimensions.

## Key findings

- Classification of boundary conditions into (2N+1) categories
- Emergence of degenerate chiral massless fermions
- Potential solutions to fermion generation and mass hierarchy problems

## 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 $(2N+1)$ 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.