Higgs mechanism near the 5d bulk phase transition

Abstract

We present a non-perturbative model of Gauge-Higgs Unification. We consider a five-dimensional pure SU(2) gauge theory with orbifold boundary conditions along the fifth dimension, such that the symmetry is reduced to U(1) at the fixed points of the orbifold action. The spectrum on the four-dimensional boundary hyperplanes includes, apart from the U(1) gauge boson, also a complex scalar, interpreted as a simplified version of the Standard Model Higgs field. The gauge theory is defined on a Euclidean lattice which is anisotropic in the extra dimension. Using the boundary Wilson Loop and the observable that represents the scalar and in the context of an expansion in fluctuations around a Mean-Field background, we show that a) near the bulk phase transition the model tends to reduce dimensionally to a four-dimensional gauge-scalar theory, b) the boundary U(1) gauge symmetry breaks spontaneously due to the broken translational invariance along the fifth dimension, c) it is possible to construct renormalized trajectories on the phase diagram along which the Higgs mass is constant as the lattice spacing is varied, d) by taking a continuum limit in the regime where the anisotropy parameter is small, it is possible to predict the existence of a Z' state with a mass around 1 TeV.