Modular symmetry anomaly in magnetic flux compactification

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(N-a) x U(N-b) thorn 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.