Modular forms of finite modular subgroups from magnetized D-brane models

Abstract

We study modular transformation of holomorphic Yukawa couplings in magnetized D-brane models. It is found that their products are modular forms, which are non-trivial representations of finite modular subgroups, e.g. $S_3$, $S_4$, $\Delta (96)$ and $\Delta (384)$.

14 pages, no figure