# Wavefunctions and Yukawa Couplings on Resolutions of $T^2/\mathbb{Z}_N$ Orbifolds

## TL;DR

This paper develops matter wavefunctions on resolved $T^2/\mathbb{Z}_N$ orbifolds with magnetic fluxes, showing how blow-up effects influence zero-mode properties, selection rules, and Yukawa couplings compared to orbifold models.

## Contribution

It introduces a method to construct wavefunctions on resolved orbifolds and analyzes how blow-up effects modify physical properties like Yukawa couplings.

## Key findings

- Blow-up effects alter zero-mode wavefunctions and selection rules.
- Yukawa couplings are affected by the resolution of orbifold singularities.
- Modular symmetry is modified due to blow-up effects.

## Abstract

We propose matter wavefunctions on resolutions of $T^2/\mathbb{Z}_N$ singularities with constant magnetic fluxes. In the blow-down limit, the obtained wavefunctions of chiral zero-modes result in those on the magnetized $T^2/\mathbb{Z}_N$ orbifold models, but the wavefunctions of $\mathbb{Z}_N$-invariant zero-modes receive the blow-up effects around fixed points of $T^2/\mathbb{Z}_N$ orbifolds. Such blow-up effects change the selection rules and Yukawa couplings among the chiral zero-modes as well as the modular symmetry, in contrast to those on the magnetized $T^2/\mathbb{Z}_N$ orbifold models.