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

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.