Cauchy Slice Holography and the Semiclassical Approximation

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. The partition function of this theory defines a natural map between the bulk canonical quantum gravity (CQG) theory Hilbert space, and the Hilbert space of the undeformed boundary CFT. We shall proceed to delve into the semiclassical approximation within Canonical Quantum Gravity (CQG). Subsequently, we aim to elucidate how the bulk is encapsulated within the correlation functions of the T^2 theory living on Cauchy slices. Based on parts of 2204.00591 with Aron Wall and Goncalo Araujo-Regado, and parts of 2309.08116.