Non-perturbative definition of five-dimensional gauge theories on the R^4 x S^1/Z_2 orbifold

TL;DR

This paper develops a non-perturbative framework for five-dimensional SU(N) gauge theories on an orbifold, showing the absence of boundary Higgs mass divergences and setting the stage for lattice studies.

Contribution

It introduces a non-perturbative construction of 5D gauge theories on an orbifold, demonstrating no boundary Higgs mass divergence and simplifying boundary conditions for lattice implementation.

Findings

No boundary mass term for the Higgs is generated.

Only Dirichlet boundary conditions are needed.

Preparation for non-perturbative lattice studies.

Abstract

We construct a Z_2 orbifold projection of SU(N) gauge theories formulated in five dimensions with a compact fifth dimension. We show through a non-perturbative argument that no boundary mass term for the Higgs field, identified with some of the fifth dimensional components of the gauge field, is generated, which would be quadratically divergent in the five-dimensional ultraviolet cutoff. This opens the possibility of studying these theories non-perturbatively in order to establish if they can be used as effective weakly interacting theories at low energies. We make preparations for a study on the lattice. In particular we show that only Dirichlet boundary conditions are needed, which specify the breaking pattern of the gauge group at the orbifold fixpoints.