1 2 3 4 5 n 1 2 3 4 5 m$_{n}$ $^{2}$GLYPH<Slash1> GeV 2 Figure 5.1: Experimentally, the ρ mesons follow very closely the relationship m 2 n ∼ n . The dots are the physical values There are still an infinite number of choices we could make for A ( z ) and Φ( z ) that would obey these constraints. We make the simplest choice, and set A ( z ) = − log( z ) and Φ = z $^{2}$. Hence the action and metric become Now we repeat the procedure of section 5.3 to find the meson masses and decay constants. Repeating the process of section 5.3.1, the equation of motion becomes As usual, we look for normalizable solutions to (5.29). However, now our choice of boundary conditions is much simpler than when there was no dilaton term. There is no hard IR cutoff at z = z$_{m}$ (as there was previously), and the action is defined for all z . So the ambiguity of (5.13) is removed when we have a theory with a smooth wall cutoff (although we have re- 81 5.5.1 Vector Mesons ∂$_{z}$ ( e − z 2 z ∂$_{z}$v$_{n}$ ) + m 2 n e − z 2 z v$_{n}$ = 0 (5.29) S = ∫ d 5 $_{x e}$− z 2 √ g Tr { | DX | 2 + 3 | X | 2 − 1 4 g 2 5 ( F 2 L + F 2 $_{R}$) } (5.27) ds 2 = 1 z 2 ( dz 2 + η$_{µν}$dx $^{µ}$dxν ) (5.28)