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Spacetime and the holographic renormalization group. (English) Zbl 0958.81046

Summary: Anti-de Sitter space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our “interior” theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.

MSC:

81T17 Renormalization group methods applied to problems in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T60 Supersymmetric field theories in quantum mechanics
83C45 Quantization of the gravitational field
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