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

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 Z(2) symmetry or Z(4) R-symmetry. We explicitly demonstrate the spontaneous CP violation on a specific Calabi-Yau threefold. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This study explores the geometrical origin of CP symmetry and spontaneous CP violation in Calabi-Yau compactifications. The CP symmetry is identified with an outer automorphism of the symplectic modular group in the large complex structure regime of Calabi-Yau threefolds. Spontaneous CP violation is realized by the introduction of fluxes, whose effective action is invariant under CP as well as discrete Z(2) symmetry or Z(4) R-symmetry.