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

Symmetry Breaking in Six Dimensional Flux Compactification Scenarios