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We review the basic notions of compactification in the presence of abackground flux. In extra-dimentional models with more than five dimensions,Scherk and Schwarz boundary conditions have to satisfy 't Hooft consistencyconditions. Different vacuum configurations can be obtained, depending whethertrivial or non-trivial 't Hooft flux is considered. The presence of the"magnetic" background flux provide, in addition, a mechanism for producingfour-dimensional chiral fermions. Particularizing to the six-dimensional case,we calculate the one-loop effective potential for a U(N) gauge theory on M4 xT2. We firstly review the well known results of the trivial 't Hooft flux case,where one-loop contributions produce the usual Hosotani dynamical symmetrybreaking. Finally we applied our result for describing, for the first time, theone-loop contributions in the non-trivial 't Hooft flux case.

One-loop effective potential in M4 x T2 with and without 't Hooft flux