Operator analysis of physical states on magnetized $T^{2}/Z_{N}$ orbifolds

TL;DR

This paper introduces an operator formalism for analyzing physical states on magnetized orbifolds, providing exact analytical results and a rigorous method for counting physical states, especially on complex geometries like $T^{2}/Z_{N}$.

Contribution

The paper presents a novel operator-based approach for analyzing states on magnetized orbifolds, applicable to complex cases and larger magnetic flux values, facilitating realistic model building.

Findings

Exact analytical results for physical states on magnetized orbifolds.

A rigorous method for counting surviving physical states.

Demonstrates the formalism's power on complex orbifold geometries.

Abstract

We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds $T^{2}/Z_{3}$, $T^{2}/Z_{4}$, $T^{2}/Z_{6}$ (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries.