Σ$_{1}$ SU (2)$_{L}$ Σ$_{2}$ Σ$_{2}$$_{N}$ Σ$_{2}$$_{N}$$_{+1}$ U (1)$_{Y}$ G$_{1}$ G$_{N}$ G$_{N}$$_{+1}$ G$_{2}$$_{N}$ U FIG. 1: Graphic representation of the moose model described by the Lagrangian given in Eq. (1) . The dashed lines represent the identification of the corresponding moose sites. III. GENERALIZATION TO 5 DIMENSIONS We now want to describe the continuum limit N → ∞ of the Lagrangian given in Eq. (1). As it is well known, a [ SU (2)] K linear moose model can be interpreted as the discretized version of a SU(2) 5D gauge theory. The GD-BESS model, however, has a number of new features with respect to a basic linear moose. In particular, we have the “cut link” and the presence of an apparently nonlocal field U which connects the gauge fields of the SU (2)$_{L}$ ⊗ U (1)$_{Y}$ local symmetry. To be able to properly describe the 5D generalization, we need a representation for the 5D metric. Since the deconstructed model possesses ordinary 4D Lorentz invariance, the extra-dimensional metric must be compatible with this symmetry. Such a metric can in general be written in the form: where η is the standard Lorentz metric with the ( − , + , + , +) signature choice, y the variable corresponding to the extra dimension and b ( y ) is a generic positive definite function, usually known as the “warp factor”. We normalize b ( y ) by requiring that b (0) = 1. For definiteness, we will consider a finite extra dimension, with y ∈ (0 , πR ). With this choice, it is possible to write down an identification between the GD-BESS and the continuum limit parameters: where g$_{5}$ is a 5D gauge coupling, with mass dimension − 1 / 2. As can be seen, a general choice for the g$_{i}$ implies that g$_{5}$ is “running” , with an explicit dependence on the extra variable. ds 2 = b ( y ) η$_{µν}$ dx $^{µ}$dxν + dy $^{2}$, (6) g 2 i N → g 2 5 πR , f 2 i → b ( y ) N πRg 2 5 , (7) 5