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Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence. (English) Zbl 0984.83043
The main issue of the present paper is to give an answer to the question “how one may obtain information about the bulk theory from CFT correlation functions”. For this the authors give a systematic method for renomalizing the AdS/CFT prescription for computing correlation functions. Using this method the authors can reconstruct the bulk spacetime metric and bulk scalar fields to the first non-trivial order. As a result it turns out that the asymptotic expansion of the corresponding bulk field near the boundary is determined by the sources of the CFT and all infrared divergences of the bulk on-shell action can be computed. Furthermore it is shown that the bulk solutions can be extended to one order further using the one-point function of the corresponding dual CFT operator. The authors have also developed some formulae for the Brown-York quasi local stress-energy tensor for an arbitrary solution of Einstein’s equations with a negative cosmological constant.

MSC:
83E05 Geometrodynamics and the holographic principle
81T20 Quantum field theory on curved space or space-time backgrounds
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