Lattice gauge theory approach to spontaneous symmetry breaking from an extra dimension

Abstract We present lattice simulation results corresponding to an SU ( 2 ) pure gauge theory defined on the orbifold space E 4 × I 1 , where E 4 is the four-dimensional Euclidean space and I 1 is an interval, with the gauge symmetry broken to a U ( 1 ) subgroup at the two ends of the interval by appropriate boundary conditions. We demonstrate that the U ( 1 ) gauge boson acquires a mass from a Higgs mechanism. The mechanism is driven by two of the extra-dimensional components of the five-dimensional gauge field which play respectively the role of the longitudinal component of the gauge boson and a massive real physical scalar, the Higgs particle. Despite the non-renormalizable nature of the theory, we observe only a mild cut-off dependence of the physical observables. We also show evidence that there is a region in the parameter space where the system behaves in a way consistent with dimensional reduction.