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

We propose a general framework for applying the pp-wave approximation to holographic calculation in the AdS/CFT correspondence. By assuming the existence and some properties of string field theory (SFT) on the AdS5×S5 background, we extend the holographic ansatz proposed by Gubser, Klebanov, Polyakov and by Witten to the SFT level. We extract relevant information about assumed SFT on AdS5×S5 from its approximation, pp-wave SFT. As an explicit example, we study conformal three point functions of BMN operators. We find a new formula which expresses a three point function as an infinite series of matrix elements of the SFT vertex. We identify a broad class of field redefinitions which do not affect the final observable. Known ambiguity in the pp-wave SFT vertex is due to a particular redefinition in this class. Under these redefinitions, matrix elements themselves change, but the sum of the series is invariant due to a non-trivial cancellation. The result agrees with that previously calculated in gauge theory.