Fixed points of Sp(4,Z) are extrema of the moduli potential in these heterotic models, with genus-2 no-go theorems for de Sitter vacua and possible metastable minima after SUSY breaking via nonperturbative Kähler terms.
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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.
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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Automorphic Structures of Heterotic Vacua
Fixed points of Sp(4,Z) are extrema of the moduli potential in these heterotic models, with genus-2 no-go theorems for de Sitter vacua and possible metastable minima after SUSY breaking via nonperturbative Kähler terms.
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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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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.