Non-perturbative Gauge-Higgs Unification

Gauge-Higgs Unification models are theories where the Higgs field is identified with some of the extra-dimensional components of the gauge field. One motivation for these models is that the extra-dimensional gauge symmetry protects the Higgs potential from divergences in the ultra-violet cut-off. Perturbative studies indicate that fermions are necessary to trigger the Higgs mechanism. Given the non-renormalizability of gauge theories in dimensions higher than four, we study non-perturbatively the simplest model which is a five-dimensional SU(2) gauge theory on a orbifold. The starting point is the formulation on an anisotropic Euclidean lattice. Results for the phase diagram, the spectrum and dimensional reduction obtained using a semi-analytic mean-field expansion and Monte Carlo simulations will be presented. These results indicate that the Higgs mechanism takes place without fermions and support an alternative view of the lattice orbifold as a five-dimensional bosonic superconductor.

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