  We discuss the gauge symmetry breaking of six dimensional theories in flux
compactification with a magnetic flux background and a constant vacuum
expectation value (VEV) for the scalar fields, which are zero modes of extra
spatial components of the gauge field. Although the effective potential for the
scalar fields are known not to be generated classically and radiatively in a
magnetic flux background only, the one-loop effective potential is shown to be
generated by the effects of the non-zero constant VEV. As illustrations, we
calculate the one-loop effective potential in SU(2) and SU(3) Yang-Mills
theories. In both cases, we find that the potential minimum is located at
non-zero VEV and the gauge symmetry breaking takes place.
