5.2 Fixing the g$_{5}$ coupling The idea in this section is to calculate the vector current two-point function in the holographic scheme, and then by equating the result to that obtained from perturbative QCD we can hence fix g$_{5}$ . We introduce the vector field as V = ( A$_{L}$ + A$_{R}$ ) / 2, choose the gauge V$_{r}$ ( x, r ) = 0, and by using the Euler-Lagrange equation on the holographic action (5.2), we obtain an equation of motion: We then substitute (5.5) back into the action (5.2), and we are left with the boundary term So, by the claim made above (5.4), equation (5.6) is the generating func- tional for QCD. To obtain the vector current two-point function, we simply functionally differentiate (5.6) twice with respect to the source V$_{0}$ , with V$_{0}$ defined in V $^{µ}$( q, z ) = V ( q, z ) V µ 0 ( q ). ( V µa 0 ( q ) is the Fourier transform of the source of the vector current J a µ = ¯ qγ$_{µ}$t $^{a}$q ).Doing the necessary maths, we get For large Euclidean Q $^{2}$( ≡ − q $^{2}$) we only need to know V ( q, r ) near the boundary, 75 [ ∂$_{z}$ ( 1 z ∂$_{z}$V a $_{µ}$( q, z ) ) + q 2 z V a $_{µ}$( q, z ) ] ⊥ = 0 (5.5) S = − 1 2 g 2 5 ∫ d $^{4}$x ( 1 z V a $_{µ}$∂$_{z}$ V µa ) ∣ z = ϵ (5.6) ∫ d $^{4}$x 〈 J a $_{µ}$( x ) J b $_{ν}$(0) 〉 = δ ab ( q$_{µ}$q$_{ν}$ − q $^{2}$g$_{µν}$ ) Π$_{V}$ ( Q $^{2}$) (5.7) 1 ∂$_{z}$V ( q, ϵ ) Π$_{V}$ ( − q $^{2}$) = − 1 g 2 $_{5}$Q 2 ∂$_{z}$V ( q, ϵ ) ϵ (5.8) V ( Q, z ) = 1 + Q $^{2}$z2 4 ln( Q $^{2}$z$^{2}$) + . . . (5.9)