Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes

Abstract

We systematically investigate possibilities of realizing the spontaneous CP violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis leads to the presence of flat directions at degenerate CP-breaking and -conserving vacua for a generic choice of three-form fluxes, indicating that flux compactifications are not sufficient to realize the spontaneous CP violation. Furthermore, the four-dimensional CP can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.

arXiv comment21 pages

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• Landscape of Modular Symmetric Flavor Models
• Modular invariant flavor model of ${\mathrm{A}}_4$ and hierarchical structures at nearby fixed points
• Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis
• A radiative seesaw model with three Higgs doublets in modular $A_4$ symmetry
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• CP Symmetry and Symplectic Modular Invariance
• Towards unification of quark and lepton flavors in $A_4$ modular invariance
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• Modular symmetry in the SMEFT
• Quark and lepton flavors with common modulus $\tau$ in $A_4$ modular symmetry
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• Time reversal and $\mathbf{CP}$ invariance in Calabi-Yau compactifications
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• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
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• Yukawa textures in modular symmetric vacuum of magnetized orbifold models