Modular design

Physics

Pure mathematics

Discrete symmetry

Symmetry (geometry)

Mathematics

Operating system

Abelian group

Geometry

Compactification (mathematics)

Theoretical physics

Computer science

Homogeneous space

Physical review. D/Physical review. D.

We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The $T^2/Z_4$ orbifold model has the same modular symmetry as the magnetized brane model with $M=2$, and its flavor symmetry $D_4$ is a subgroup of the modular symmetry.

Modular symmetry and non-Abelian discrete flavor symmetries in string compactification