Modular symmetry of localized modes

TL;DR

This paper investigates the modular symmetry properties of localized modes on a specific orbifold, revealing their associated flavor symmetries and providing explicit wave functions, which advances understanding of symmetry structures in string-inspired models.

Contribution

It identifies the modular flavor symmetries of localized modes on $T^2/\mathbb{Z}_2$ orbifold and derives explicit wave functions, highlighting new symmetry patterns.

Findings

Localized modes with even modular weight have $\Delta(6n^2)$ symmetry.

Localized modes with odd modular weight have $\Delta'(6n^2)$ symmetry.

Explicit wave functions of localized modes are provided.

Abstract

We study the modular symmetry of localized modes on fixed points of $T^2/\mathbb{Z}_2$ orbifold. First, we find that the localized modes with even (odd) modular weight generally have $\Delta(6n^2)$ ($\Delta'(6n^2)$) modular flavor symmetry. Moreover, when we consider an additional Ansatz, the localized modes with even (odd) modular weight generally enjoy $S_3$ ($S'_4$) modular flavor symmetry, and we show the concrete wave functions of the localized modes.