A benchmark model using genus-2 modular invariance generates quark mass hierarchies and CP violation via moduli VEVs near invariant points, with mass ratios vanishing in the symmetric limit and mixing angles reproduced.
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Incomplete zero-mode multiplets under Scherk-Schwarz phases in magnetized compactifications violate modular symmetry as a group but retain control over couplings via full modular forms.
Blow-up of magnetized T²/Z_N preserves total magnetic flux, total curvature, and effective flux on connecting lines, while the number of localized modes at each singularity increases by one per mass level increment.
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Quark hierarchies and CP violation from the Siegel modular group
A benchmark model using genus-2 modular invariance generates quark mass hierarchies and CP violation via moduli VEVs near invariant points, with mass ratios vanishing in the symmetric limit and mixing angles reproduced.
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More about modular symmetries and non-invertible properties in magnetized compactifications
Incomplete zero-mode multiplets under Scherk-Schwarz phases in magnetized compactifications violate modular symmetry as a group but retain control over couplings via full modular forms.
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Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
Blow-up of magnetized T²/Z_N preserves total magnetic flux, total curvature, and effective flux on connecting lines, while the number of localized modes at each singularity increases by one per mass level increment.