16 V. LOW ENERGY LIMIT AND EW PRECISION OBSERVABLES We can obtain a convenient low-energy approximation of the theory by using the so- called holographic approach [25, 63, 64, 70–73], which consists in integrating out the bulk degrees of freedom in the functional integral. For the purposes of the present calculation it is sufficient to take into account just the tree-level effects of the heavy resonances, so the integration can be done by simply eliminating the bulk fields from the Lagrangian via their classical equations of motion; moreover, bulk gauge self-interactions can be neglected. The equations to be solved are: with ˆ D defined in eq. (16)) and we have Fourier transformed with respect to the first four coordinates. As previously discussed, on the y = 0 brane, we do not want to make any assumptions on the value of the fields; so we leave their variations arbitrary, and since there are no localized terms on the brane, this leads to Neumann boundary conditions for all of the fields: $^{∂$_{y}$}$$^{W}$$^{a}$ R µ At the other end of the AdS segment, we account for the presence of localized terms by imposing four fields to be equal to generic source fields , while the other two (those corre- sponding to the right charged sector) are vanishing: The first step in solving the equations is to split the fields in their longitudinal (aligned with p$_{µ}$ ) and transverse parts. The operator ( p $^{2}$δ$_{µν}$ − p$_{µ}$p$_{ν}$ ) is vanishing when acting on the longitudinal part, while it is simply equivalent to p 2 when acting on the transverse one. In this way, each equation can be split into two simpler ones: ˆ D W a L ( R ) $_{µ}$( p, y ) = ( p $^{2}$δ$_{µν}$ − p$_{µ}$p$_{ν}$ ) W a ν L ( R $_{)}$( p, y ) (49)   L µ = 0 ∂$_{y}$W a R µ = 0 y = 0 . (50)     $^{W}$$^{a}$ L µ = ˜ W a µ W 3 R µ = ˜ B$_{µ}$ W 1 , 2 R µ = 0 y = πR. (51)    ˆ D W a, tr L/R µ = p $^{2}$W a, tr L/R µ ˆ D W a, long L/R µ = 0 (52)