Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications

Keiya Ishiguro, Tatsuo Kobayashi, Hajime Otsuka

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


We explore the geometrical origin of CP and the spontaneous CP violation in Calabi-Yau compactifications. We find that the CP symmetry is identified with an outer automorphism of the symplectic modular group in the large complex structure regime of Calabi-Yau threefolds, thereby enlarging the symplectic modular group to their semidirect product group. The spontaneous CP violation is realized by the introduction of fluxes, whose effective action is invariant under CP as well as the discrete Z2 symmetry or Z4 R-symmetry. We explicitly demonstrate the spontaneous CP violation on a specific Calabi-Yau threefold.

Original languageEnglish
Article number115598
JournalNuclear Physics B
Publication statusPublished - Dec 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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