Generation structures and Yukawa couplings in magnetized $T^{2g}/\mathbb{Z}_N$ models

TL;DR

This paper investigates fermion zero-mode wave functions and Yukawa couplings in magnetized higher-dimensional tori, analyzing their properties under various transformations and orbifold constructions to understand their structure in string-inspired models.

Contribution

It provides a detailed analysis of zero-mode wave functions, their transformation properties, and Yukawa couplings in magnetized $T^{2g}$ models, including orbifold constructions and sector analysis.

Findings

Explicit wave functions satisfying Dirac and boundary conditions

Transformation properties under modular and parity operations

Counting of wave functions in orbifold sectors

Abstract

We study fermion zero-mode wave functions with various chiralities in magnetized $T^{2g}$, $(g=2,3)$ torus. First, we consider the wave functions satisfying the Dirac equation and the boundary conditions on the magnetized torus. Second, we introduce the $SO(3)$ (or parity) transformations and derive the wave functions under the modular transformation. Additionally, we calculate the Yukawa couplings with consideration for the chirality. Lastly, we briefly review how to construct $T^{4}/\mathbb{Z}_N$ ($N=2,3,4,6$) and $T^6/\mathbb{Z}_{12}$ twisted orbifold. Also, we explicitly analyze the number of the wave functions in $\mathbb{Z}_N$ sectors.