We study Gauge-Higgs Unification in five dimensions on the lattice by means of the meanfield expansion. We formulate it for the case of an SU(2) pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1) on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is nonzero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations [12].

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.Comment: 14 pages, 8 figure

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We present novel calculations of the mass hierarchy of the SU(2) pure gauge theory on a spacetime lattice with an orbifolded fifth dimension. This theory has three parameters; the gauge coupling β , the anisotropy γ, which is a measure of the ratio of the lattice spacing in the four dimensions to that in the fifth dimension, and the extent of the extra dimension N 5 . Using a large basis of scalar and vector operators we explore in detail the spectrum along the γ = 1 line, and for the first time we investigate the spectrum for γ = 1.