For a Few Symmetries More ... or How to Compute the Higgs Mass

The new idea of deconstruction allows to realize the physics of extra dimensions in a strictly four dimensional set-up. After a short review of these techniques extended to supersymmetry, I will report on an application to build models in which the low energy spectrum shows no sign of supersymmetry but still the radiative corrections to the mass parameters are weakly dependent on the cutoff scale, if this one remains low enough. As a consequence, the Higgs mass dependence in high energy physics is effectively parametrized by the deconstruction scale which also fixes the gauge boson masses through the Higgs vacuum expectation value. In this regard, deconstruction, somehow as gauge in variance, is a dynamical principle that dictates the interactions of particles and gauge fields at low energy and quantum level. (author)