Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
Keiya Ishiguro, Tatsuo Kobayashi, Hajime Otsuka
Abstract
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.
Topics & Concepts
Calabi–Yau manifoldSemidirect productSymplectic geometryDiscrete symmetryPhysicsPure mathematicsSymmetry (geometry)AutomorphismInvariant (physics)Homogeneous spaceMathematicsGroup (periodic table)Mathematical physicsQuantum mechanicsGeometryBlack Holes and Theoretical PhysicsAtomic and Subatomic Physics ResearchAdvanced NMR Techniques and Applications