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.


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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