Preprint number: CP3-Origins-2012-21 and DIAS-2012-22
We investigate generic properties of the conformal phase transition in gauge theories featuring Higgs-like fundamental particles. These theories provide an excellent arena to properly investigate conformal dynamics and discover novel features. We show, on general grounds, that the phase transition at the boundary of the Higgs conformal window is, except in special cases, of jumping type. This implies that the massive spectrum of the theory will jump at the phase transition. Jumping, however, still allows for one of the states, the would be dilaton of the theory, to be lighter than the heaviest states in the broken phase. Finally we also exhibit a calculable Higgs model in which we can, in perturbation theory, determine the Higgs conformal window, the spectrum in the conformally broken phase and demonstrate to possess a jumping type conformal phase transition.