  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. We explore the Nielsen-Olesen instability for SU(N)
on a torus, in the presence of a magnetic background. A field theory approach
is developed, computing explicitly the minimum of the complete effective
potential, including tri-linear and quartic couplings and determining the
symmetries of the stable vacua. We also develop appropriate gauge-fixing terms
when both Kaluza-Klein and Landau levels are present and interacting,
discussing the interplay between the possible six and four dimensional choices.
The equivalence between coordinate dependent and constant Scherk-Schwarz
boundary conditions -associated to either continuous or discrete Wilson lines-
is analyzed.
