at the scale of matching to the strongly coupled regime of QCD. We leave attempts to further improve the UV of the theory to chapter 7. Finally, as we showed in section 5.5, an appropriate change to the IR behaviour of the dilaton can correct the n scaling of the tower of excited ρ meson states. We have tested our model in this respect but find only a marginal improvement over the pure AdS case. This is a sign that, although our geometry describes a non-supersymmetric gauge configuration, it is still not a perfect description of QCD and work remains to be done on improving the geometric background. For a generic five dimensional holographic model of QCD, we can write the action as with D$_{µ}$U = ∂$_{µ}$U − iA$_{Lµ}$U + iUA$_{Rµ}$ . The field U ( x, r ) = exp( iπ $^{a}$( x, r ) T $^{a}$) describes the pions produced by the breaking of a U ( N$_{f}$ ) chiral symmetry with generators T $^{a}$. The non-Abelian gauge fields A$_{L}$ and A$_{R}$ couple by left and right action on U and holographically describe the axial and vector mesons (we describe this in more detail later). The σ is a Higgs-like field and we only consider fluctuations in its r direction. It holographically describes the quark mass and condensate. A non-zero value for this field will break the U ( N$_{f}$ )$_{L}$ × U ( N$_{f}$ )$_{R}$ symmetry of the action down to U ( N$_{f}$ )$_{V}$ . If we set φ = 0 and L σ = 3 | X | $^{2}$, we reproduce the model discussed in chapter 5. However, in this chapter, we are going to use a compactified model of 88 6.1 The generic 5D holographic model S ∼ ∫ d $^{4}$x dr e φ √ − g ( L σ + Tr | DX | 2 − 1 4 g 2 5 Tr( F 2 L + F 2 $_{R}$) ) (6.1)