Extra-dimensional models on the lattice

Abstract

In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergencies by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include non-perturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.

Review published on the International Journal of Modern Physics A for the special issue "Lattice gauge theory beyond QCD". 22 pages and 7 figures

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• Status of the asymptotic safety paradigm for quantum gravity and matter
• Brout-Englert-Higgs physics: From foundations to phenomenology
• Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
• Lattice Simulations of 10d Yang-Mills toroidally compactified to 1d, 2d and 4d
• Collider signals of $W^{\prime }$ and $Z^{\prime }$ bosons in the gauge-Higgs unification
• RG flows in Non-Perturbative Gauge-Higgs Unification I
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• The Higgs phase as a spin glass phase in D=5 dimensional SU(2) gauge Higgs theory
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Constrained Hybrid Monte Carlo algorithms for gauge-Higgs models