Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$

TL;DR

This paper investigates the behavior of massive modes on a magnetized blow-up manifold derived from a $T^2/\mathbb{Z}_N$ orbifold, focusing on the effects of the blow-up process on mode localization and flux invariance.

Contribution

It establishes conditions for smooth mode connection during blow-up and reveals how localized mode counts change with mass levels.

Findings

Number of localized modes increases by one per mass level increment.

Magnetic flux and curvature invariants are preserved during blow-up.

Smooth connection between modes on orbifold and blown-up manifold is achieved.

Abstract

We study massive modes on a magnetized blow-up manifold of $T^2/\mathbb{Z}_N$. The blow-up manifold can be constructed by appropriately replacing orbifold singular points with a part of $S^2$. To ensure a smooth connection between the massive modes on magnetized $T^2/\mathbb{Z}_N$ orbifold and those on magnetized $S^2$, it is required that not only the total magnetic flux as well as the total curvature but also the effective magnetic flux on the connected line remain invariant under the blow-up procedure. Furthermore, we find that the number of the localized modes at each orbifold singular point increases by one for each unit increment of the mass level.