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We study modular symmetry anomalies in four-dimensional low-energy effective field theory, which is derived from six-dimensional supersymmetric U (N) Yang-Mills theory by magnetic flux compactification. The gauge symmetry U (N) is broken to U (N₀) (N₁) by magnetic fluxes. It is found that an Abelian subgroup of the modular symmetry corresponding to discrete part of U (1) can be anomalous, but other elements independent of U (1) in the modular symmetry are always anomalyfree.
Kariyazono et al. (Thu,) studied this question.