Holography at string field theory level: Conformal three point functions of BMN operators

A general framework for applying the pp-wave approximation to holographic calculations in the AdS/CFT correspondence is proposed. By assuming the existence and some properties of string field theory (SFT) on $AdS_5 \times S^5$ background, we extend the holographic ansatz proposed by Gubser, Klebanov, Polyakov and Witten to SFT level. We extract relevant information of assumed SFT on $AdS_5 \times S^5$ from its approximation, pp-wave SFT. As an explicit example, we perform string theoretic calculations of the conformal three point functions of the BMN operators. The results agree with the previous calculations in gauge theory. We identify a broad class of field redefinitions, including known ambiguities of the interaction Hamiltonian, which does not affect the results.