Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation

TL;DR

This paper investigates fermion zero-modes on magnetized $T^4/Z_N$ orbifolds, using modular transformations to analyze their number and conditions for three-generation models, and explores parity transformations to understand chirality relations.

Contribution

It introduces a method using $Sp(4, ext{Z})$ modular transformations to analyze zero-modes and clarifies conditions for realizing three-generation models on these orbifolds.

Findings

Number of zero-modes analyzed via modular transformations.

Conditions for three-generation models clarified.

Parity transformations relate positive and negative chirality wavefunctions.

Abstract

We study fermion zero-mode wavefunctions on $T^4/Z_N$ orbifold with background magnetic fluxes. The number of zero-modes is analyzed by use of $Sp(4,\mathbb{Z})$ modular transformation. Conditions needed to realize three generation models are clarified. We also study parity transformation in the compact space which leads to better understanding of relationship between positive and negative chirality wavefunctions.