# Modular symmetry anomaly in magnetic flux compactification

## TL;DR

This paper investigates anomalies in modular symmetry within a four-dimensional effective field theory derived from six-dimensional supersymmetric Yang-Mills theory, focusing on how magnetic fluxes influence symmetry anomalies.

## Contribution

It reveals that the Abelian subgroup of the modular symmetry associated with the discrete part of $U(1)$ can be anomalous, while other elements remain anomaly-free.

## Key findings

- Abelian subgroup of modular symmetry can be anomalous
- Non-Abelian elements of modular symmetry are anomaly-free
- Magnetic fluxes break gauge symmetry to $U(N_a) imes U(N_b)$

## 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 $U(N_a) \times U(N_b)$ by magnetic fluxes. It is found that 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 anomaly-free.