4D modular flavor symmetric models inspired by higher dimensional theory

TL;DR

This paper explores deriving 4D modular flavor symmetric models from higher-dimensional theories, where wavefunctions in extra dimensions are modular forms, imposing new constraints on matter field representations.

Contribution

It introduces a scenario connecting higher-dimensional theories with 4D modular flavor models, highlighting the role of wavefunctions as modular forms and their impact on matter field representations.

Findings

Wavefunctions in extra dimensions are modular forms.

Constraints on modular weights and matter representations.

Examples illustrating the proposed scenario.

Abstract

We study a scenario to derive four-dimensional modular flavor symmetric models from higher dimensional theory by assuming the compactification consistent with the modular symmetry. In our scenario, wavefunctions in extra dimensional compact space are modular forms. That leads to constraints on combinations between modular weights and $\Gamma_N$ ($\Gamma_N')$ representations of matter fields. We also present illustrating examples.