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We examine a common origin of four-dimensional flavor, CP, and $U(1)_R$symmetries in the context of heterotic string theory with standard embedding.We find that flavor and $U(1)_R$ symmetries are unified into the $Sp(2h+2,\mathbb{C})$ modular symmetries of Calabi-Yau threefolds with $h$ being thenumber of moduli fields. Together with the $\mathbb{Z}_2^{\rm CP}$ CP symmetry,they are enhanced to $GSp(2h+2, \mathbb{C})\simeq Sp(2h+2, \mathbb{C})\rtimes\mathbb{Z}_2^{\rm CP}$ generalized symplectic modular symmetry. We exemplifythe $S_3, S_4, T^\prime, S_9$ non-Abelian flavor symmetries on explicittoroidal orbifolds with and without resolutions and $\mathbb{Z}_2,S_4$ flavorsymmetries on three-parameter examples of Calabi-Yau threefolds. Thus,non-trivial flavor symmetries appear in not only the exact orbifold limit butalso a certain class of Calabi-Yau threefolds. These flavor symmetries arefurther enlarged to non-Abelian discrete groups by the CP symmetry.

Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries