Layered Higgs phase as a possible field localization on a brane

So far it has been found by using lattice techniques that in the anisotropic five-dimensional Abelian Higgs model, a layered Higgs phase exists in addition to the expected five-dimensional one. The exploration of the phase diagram has shown that the two Higgs phases are separated by a phase transition from the confining phase. This transition is known to be first order. In this paper we explore the possibility of finding a second-order transition point in the critical line that separates the first-order phase transition from the crossover region. This is shown to be the case only for the four-dimensional Higgs layered phase while the phase transition to the five-dimensional broken phase remains first order. The layered phase serves as the possible realization of four-dimensional spacetime dynamics, which is embedded in a five-dimensional spacetime. These results are due to gauge and scalar field localization by confining interactions along the extra fifth direction