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Cauchy Slice Holography: A New AdS/CFT Dictionary

Goncalo Araujo-RegadoRifath KhanAron C. Wall
摘要
We investigate a new approach to holography in asymptotically AdS spacetimes,in which time rather than space is the emergent dimension. By making asufficiently large T^2-deformation of a Euclidean CFT, we define a holographictheory that lives on Cauchy slices of the Lorentzian bulk. (More generally, foran arbitrary Hamiltonian constraint equation that closes, we show how to obtainit by an irrelevant deformation from a CFT with suitable anomalies.) Thepartition function of this theory defines a natural map between the bulkcanonical quantum gravity theory Hilbert space, and the Hilbert space of theusual (undeformed) boundary CFT. We argue for the equivalence of the ADM andCFT Hamiltonians. We also explain how bulk unitarity emerges naturally, eventhough the boundary theory is not reflection-positive. This allows us toreformulate the holographic principle in the language of Wheeler-DeWittcanonical quantum gravity. Along the way, we outline a procedure for obtaining a bulk Hilbert space fromthe gravitational path integral with Dirichlet boundary conditions. Followingprevious conjectures, we postulate that this finite-cutoff gravitational pathintegral agrees with the T^2-deformed theory living on an arbitrary boundarymanifold -- at least near the semiclassical regime. However, the T^2-deformedtheory may be easier to UV complete, in which case it would be natural to takeit as the definition of nonperturbative quantum gravity.
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