  Motivated by the electroweak hierarchy problem, we consider theories with two
extra dimensions in which the four-dimensional scalar fields are components of
gauge boson in full space, namely the Gauge-Higgs unification framework. We
briefly explain the basics features of "flux compactification", i.e.
compactification in presence of a background (magnetic) flux. In particular we
recall how chirality and symmetry breaking can be obtained in this context.
More in details, we find and catalogue all possible degenerate zero-energy
stable configurations in the case of trivial or non-trivial 't Hooft flux, for
a SU(N) gauge theory on a torus. We describe the residual symmetries of each
vacua and the four-dimensional effective spectrum in terms of continuous and
discrete parameters, respectively.
