four large dimensions, $z$ parameterizes the coordinate along the extra dimension, and $\eta_{\mu \nu} = Diag(-, +, +, +)$ is the four-dimensional metric. Greek letters denote the four large dimensions $0,1,2,3$ and capital roman letters include the fifth dimension as well. The UV boundary is at $z_h = 1/ \kappa$ where the scale factor $(z_h / z)^2 = 1$ and the IR boundary is at $z_v \sim 1 / {\rm TeV}$, as motivated by the hierarchy problem.

We are particularly interested in a model where all Standard Model (SM) fields, except perhaps the Higgs, propagate in the entire 5-d spacetime, and will be primarily concerned with the gluon and colored fermion fields. The action for the gauge fields and fermions is, S = d\^5x {- F\_[MN]{}\^[a]{}F\^[MN a]{} + i \^ e\_\^[M]{} D\_M + i c } . \[eq:action0\] where $\Gamma^{\dot{M}}$ are the 5d ($4 \times 4$) Dirac matrices, $e_{\dot{M}}^{M}$ is the veilbein, $a$ is an adjoint gauge index and $c$ parameterizes the magnitude of a bulk mass for the fermion in units of the curvature.

We work in a unitary gauge $A_5 = 0$, and decompose the 5d fields in KK modes, A\^a\_(x,z) = \_n A\^[a(n)]{}\_(x) g\^[(n)]{}(z) ,\
\_[L,R]{} (x,z) 