We study the modular symmetry in magnetized compactifications. The zero-modes with different Scherk-Schwarz phases transform one another. A generic model does not include modes with all the Scherk-Schwarz phases. Incomplete multiplet representations appear. The modular group is violated, but the modular symmetry still controls coupling terms in those models. Modular forms of the full symmetry appear as coupling constants.
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Kobayashi et al. (2026) studied this question.
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