and, of course, in the UV the Higgs-like field must asymptote to the usual holographic quark mass ( m$_{q}$ ) and condensate ( σ ) terms: Unfortunately, although it is not yet clear, including the dilaton term in the action (5.27) ruins the predictability of the axial vector meson sector. We demonstrate why in the next section. For large z , the equation of motion for X ( z ) (5.34) becomes (5.36) has two linearly independent solutions. One asymptotes to e z 2 in the IR, whilst the other tends to e − 0 . 75 z − $^{2}$. The solution must be finite for all z , so we must discard the first solution, and hence conclude that m$_{q}$ and σ are proportional to one another. This is not what one wants in a theory with anomalous symmetry breaking. We conclude that including a dilaton term Φ( z ) = − z 2 greatly improves the vector meson sector, but removes anomalous symmetry breaking from the holographic field theory. We only included terms quadratic in X in the holographic action (5.27). The previous section showed that this is not sufficient to model the axial vector meson well. Including such terms would introduce nonlinearity into equation (5.34). This in turn would make the relationship between m$_{q}$ and σ nonlinear: an essential result if we are to holographically model spontaneous symmetry breaking. This avenue is left to other authors. 83 Further extensions Loss of predictability $^{$_{X}$′′}$− 2 $_{zX}$′ + 3 z $_{2}$X = 0 ( z ≫ 1) (5.36) X ( z ) z → 0 −→ 1 2 m$_{q}$z + 1 2 σz 3 (5.35)