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At large energies, the relevant operator does not affect the field theory, so the UV region of the dual geometry of the perturbed CFT (i.e. close to the boundary) is simply AdS. However, when following the RG flow, at some scale the effects of the perturbation set in, this is where the geometry is deformed. For a mass perturbed CFT below the mass scale, the ...


I feel like this is an over-simplification. I agree. IMHO it's a popscience analogy that's presented as a genuine explanation, but it isn't. What is lost in the actual AdS/CFT correspondence in this analogy? A dimension. You can't just discard this. If you do, you lay yourself wide open to dropping another dimension, and saying the flat 2D image is ...

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