Table 7.1: Preferred values for: a) the quantum dimension ω of the operator ¯ qγ $^{µ}$q (left), and b) the field dual to G Tr F 4 (right) four. Therefore it is identified with the coupling G of the operator Tr F $^{4}$. We repeated the fit to the lightest five ρ mesons masses in this deformed geometry. The results are displayed in table 7.1(b). The results show two effects. Firstly that α grows as Λ decreases. This is to be expected since α changes the large r part of the metric. To change the results when only a small r slice of the metric is present needs a large α . Secondly, the result at Λ = 194 MeV is an exception to this rule. In fact changing α in this case only has an effect on the third significant figure in the error. This reflects just how good the fit is from a simple cutoff. We conclude that at an appropriately low cutoff, the influence of the G Tr 4 is a small effect. A perturbative gravitational dual of QCD should only be expected to work at energies below a few GeV at best, where QCD is non-perturbative. We have investigated imposing a UV cutoff on an AdS/QCD model of the ρ mesons and found that the data has a fit at the 2% level with a UV cutoff of a few hundred MeV (compared to a fit of 21% with an infinite cutoff). This leads us to the conclusion that the holographic description of QCD should only be used at low energies on a quite small radial interval. However this 104 7.6 Discussion Λ /MeV α ϵ$_{rms}$ /% 11000 0.0011 8.2 5600 0.0045 7.5 2700 0.019 6.8 470 0.75 4.7 194 0.08 1.8 meson ω ρ ∗ 1.85 ρ ∗∗ 1.98 ρ ∗∗∗ 2.12 ρ ∗∗∗∗ 1.98