Modular symmetry of localized modes

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 $\Delta (6n^2)$ (${\Delta }^{\prime }(6n^2)$) modular flavor symmetry. Moreover, when we consider an additional Ansatz, the localized modes with even (odd) modular weight generally enjoy $S_3$ ($S_4^{\prime }$) modular flavor symmetry, and we show the concrete wave functions of the localized modes.

Comments: 18 pages