For arbitrary spin and to all orders in an external source, the boundary limit of conformally smeared bulk operators equals the CFT generating functional, so the GKP-Witten relation follows from symmetry and OPE alone.
Holographic computation of quantum corrections to the bulk cosmological constant
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abstract
We explore the program of the construction of the dual bulk theory in the flow equation approach. We compute the vacuum expectation value of the Einstein operator at the next to leading order in the 1/n expansion using a free O(n) vector model. We interpret the next to leading correction as the quantum correction to the cosmological constant of the AdS space. We finally comment on how to generalize this computation to matrix elements of the Einstein operator for excited states.
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Derivation of the GKP-Witten relation by symmetry without Lagrangian
For arbitrary spin and to all orders in an external source, the boundary limit of conformally smeared bulk operators equals the CFT generating functional, so the GKP-Witten relation follows from symmetry and OPE alone.