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## 7.4 Anomalous Dimensions at the Cutoff Scale 

There remains the possibility that the classical dimension of any operator is not respected at the quantum level. Here we investigate possible effects to the operator ¯ qγ $^{µ}$q ∗ . Classically is has dimension three, and this is encoded in the gravity dual by fixing the UV boundary condition as 

In general though we should write 

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and numerically investigate the preferred value of ω . The result is that for all values of the cutoff, from ∞ down to our tuned value of 194 MeV, the preferred value of ω is two, so it appears that the classical value is conserved at the quantum level. 

However, this is a rather naive analysis: if one evaluates the derivative of the flows f$_{n}$ ( r ) at finite values of r in the case of the model with an infinite cutoff, the derivatives differ for each value of n . Hence we should be 

