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.
Highlights
Understanding the origin of CP violation in the Standard Model (SM) is of particular interest, to explain the structure of Yukawa couplings and to search for new physics beyond the SM through experiments on the neutron electric dipole moment [1], K meson decays, and observations of the excess of baryons over antibaryons in the Universe
We systematically investigated whether the spontaneous CP violation can be realized in Type IIB flux compactifications on toroidal orientifolds, which allow for the stabilization of the moduli in a controlled way
Similar to the heterotic string theory, 4D CP is regarded as a discrete gauge symmetry embedded into the 10D proper Lorentz symmetry
Summary
Understanding the origin of CP violation in the Standard Model (SM) is of particular interest, to explain the structure of Yukawa couplings and to search for new physics beyond the SM through experiments on the neutron electric dipole moment [1], K meson decays (probed by the KOTO experiment at the J-PARC and the NA62 experiments at CERN), and observations of the excess of baryons over antibaryons in the Universe. The purpose of this paper is to systematically investigate the possibilities of realizing the spontaneous CP violation in Type IIB string theory on toroidal orientifolds, where the moduli stabilization as well as the calculation of Yukawa couplings is performed in a controlled way. Since it is possible to stabilize these axionic fields by three-form fluxes in the low-energy effective action of Type IIB string theory, we search for CP-breaking minima in Type IIB flux compactifications on several toroidal orientifolds. We review the low-energy effective action of magnetized D-branes in Type IIB string theory on toroidal orientifolds with a special emphasis on 4D CP. The CKM phase in Yukawa couplings of chiral zero modes on magnetized D7-branes is determined by one of the closed string moduli, namely the complex structure moduli τi associated with tori ðT2Þi.
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