Extra-dimensional models on the lattice

TL;DR

This review discusses lattice simulation efforts in extra-dimensional gauge theories, focusing on gauge-Higgs unification, non-perturbative effects, and the transition from perturbative to strongly-coupled regimes.

Contribution

It provides a comprehensive summary of lattice studies on extra-dimensional models, highlighting non-perturbative insights beyond traditional perturbation theory.

Findings

Lattice simulations reveal non-perturbative effects in gauge-Higgs unification.

Perturbative predictions may not hold in strongly-coupled regimes.

Dimensional reduction mechanisms are explored through numerical methods.

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.