Modular symmetry anomaly in magnetic flux compactification

Abstract

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 $U({N}_{a})\ifmmode\times\else\texttimes\fi{}U({N}_{b})$ 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.