Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence

Abstract

The issue of holographic mapping between bulk and boundary in the plane-wave limit of AdS/SYM correspondence is reexamined from the viewpoint of correlation functions. We first study the limit of large angular momentum for the so-called GKP-W relation in supergeravity approximation, connecting directly the effective action in the bulk and the generating functional of correlation functions on the boundary. The spacetime tunneling picture which has been proposed in our previous works naturally emerges. This gives not only a justification of our previous proposal, with some important refinements, on the mapping between bulk effective interaction and the CFT coefficients on the boundary in the plane-wave limit, but also implies various insights on the interpretation of holography in the plane-wave limit. Based on this result, we construct a new `holographic' string field theory. We confirm for several nontrivial examples that this gives the CFT coefficients derived by perturbation theory on the gauge-theory side. Our results are useful for understanding how apparently different duality maps proposed from different standpoints are consistent with each other and with our definite spacetime picture for the AdS holography in the plane-wave limit.