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

Keiya Ishiguro, Tatsuo Kobayashi, Hajime Otsuka

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


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, ℂ) modular symmetries of Calabi-Yau threefolds with h being the number of moduli fields. Together with the ℤ2CP CP symmetry, they are enhanced to GSp(2h + 2, ℂ) ≃ Sp(2h + 2, ℂ) ⋊ ℤ2CP generalized symplectic modular symmetry. We exemplify the S3, S4, T′, S9 non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and ℤ2, S4 flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau three-folds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

Original languageEnglish
Article number20
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - Jan 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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