Cauchy Slice Holography: A New AdS/CFT Dictionary

Understand

We investigate a new approach to holography in asymptotically AdS spacetimes, in which time rather than space is the emergent dimension.

• By making a sufficiently large T^2-deformation of a Euclidean CFT, we define a holographic theory that lives on Cauchy slices of the Lorentzian bulk.
• (More generally, for an arbitrary Hamiltonian constraint equation that closes, we show how to obtain it by an irrelevant deformation from a CFT with suitable anomalies.) The partition function of this theory defines a natural map between the bulk canonical quantum gravity theory Hilbert space, and the Hilbert space of the usual (undeformed) boundary CFT.
• We argue for the equivalence of the ADM and CFT Hamiltonians.