It is considered that AdS/CFT correspondence is a geometrization of the RG flow.

In a RG flow, knowing the physics at a length scale \(z_0\) means that one knows the physics at all length scales \(z \geq z_0\)

So, is it possible that there exist a kind of "inside-AdS" correspondence that could be written :

\(AdS_{| { z \geq z_0}}\) / \((AdS \, slice)_{z=z_0}\), so that, in some sense, one recovers the AdS/CFT correspondence in the limit \(z_0 \to 0\).

If it makes sense, does this mean that there are possible relations between the AdS on-shell fields at \(z \geq z_0\), and the AdS off-shell fields at \(z = z_0\)?