English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study $T^2/Z_N$ orbifold models with magnetic fluxes. We propose asystematic way to analyze the number of zero-modes and their wavefunctions byuse of modular transformation. Our results are consistent with the previousresults, and our approach is more direct and analytical than the previous ones.The index theorem implies that the zero-mode number of the Dirac operator on$T^2$ is equal to the index $M$, which corresponds to the magnetic flux in acertain unit. Our results show that the zero-mode number of the Dirac operatoron $T^2/Z_N$ is equal to $\lfloor M/N \rfloor +1$ except one case on the$T^2/Z_3$ orbifold.

Zero-modes on orbifolds : magnetized orbifold models by modular transformation