  We study a scalar zero mode originated from extradimensional components of a
gauge field in a six-dimensional theory compactified on a magnetized torus. We
confirm it is a Nambu-Goldstone boson of the translational symmetry on the
torus which is breaking spontaneously due to magnetic flux. We also show
explicitly it is massless up to the two-loop level. Moreover, we discuss full
order contributions by considering the effective potential.
