Modular weights of wave functions on magnetized torus

TL;DR

This paper investigates the relationship between modular weights and mass levels of wave functions in magnetized torus models, extending the analysis to higher-dimensional cases and constructing excited state wave functions.

Contribution

It explicitly demonstrates the equivalence of modular weights and mass levels in magnetized T^2 models and extends this to T^{2g} models, including excited states.

Findings

Modular weights of wave functions are equivalent to their mass levels.

Extended the equivalence to magnetized T^{2g} models.

Constructed wave functions for excited states in higher-dimensional models.

Abstract

We study the origin of modular weights of wave functions in magnetized $T^{2}$ models. It is explicitly demonstrated that the modular weights of the wave functions on magnetized $T^2$ is equivalent to their mass level. We further extend this result to magnetized $T^{2g}$ models. As a result, we construct the wave functions of excited states in magnetized $T^{2g}$ models and show that their modular weights are likewise equivalent to the corresponding mass levels.