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In this paper, we extend the Hamilton-Kabat-Lifschytz-Lowe (HKLL) holographic smearing function method to reconstruct (quasi)local anti-de Sitter bulk scalar observables in the background of a large anti-de Sitter black hole formed by null shell collapse (a "pure state" black hole), from the dual conformal field theory which is undergoing a sudden quench. In particular, we probe the near horizon and subhorizon bulk locality. First, we construct local bulk operators from the conformal field theory in the leading semiclassical limit, N → ∞. Then, we look at effects due to the finiteness of N, where we propose a suitable coarsegraining prescription involving early and late time cutoffs to define semiclassical bulk observables which are approximately local, their departure from locality being nonperturbatively small in N. Our results have important implications on the black hole information problem. [ABSTRACT FROM AUTHOR]

Most of the literature in the bulk reconstruction program in holography focuses on recovering local bulk operators propagating on a quasilocal bulk geometry and the knowledge of the bulk geometry is always assumed or guessed. The fundamental problem of the bulk reconstruction program, which is recovering the bulk background geometry (metric) from the boundary CFT state is still outstanding. In this work, we formulate a recipe to extract the bulk metric itself from the boundary state, specifically, the modular Hamiltonian information of spherical subregions in the boundary. Our recipe exploits the recent construction of Kabat and Lifschytz [J. High Energy Phys. 06 (2017) 120.] to first compute the bulk two point function of scalar fields directly in the CFT without knowledge of the bulk metric or the equations of motion, and then to take a large scaling dimension limit (WKB) to extract the geodesic distance between two close points in the bulk i.e., the metric. As a proof of principle, we consider three dimensional bulk and selected CFT states such as the vacuum and the thermofield double states. We show that they indeed reproduce the pure AdS and the regions outside the Rindler wedge and the BTZ black hole up to a rigid conformal factor. Since our approach does not rely on symmetry properties of the CFT state, it can be applied to reconstruct asymptotically AdS geometries dual to arbitrary general CFT states provided the modular Hamiltonian is available. We discuss several obvious extensions to the case of higher spacetime dimensions as well as some future applications, in particular, for constructing metric beyond the causal wedge of a boundary region. In the process, we also extend the construction of Kabat and Lifschytz [J. High Energy Phys. 06 (2017) 120.] to incorporate the first order perturbative locality for AdS scalars. [ABSTRACT FROM AUTHOR]

We outline a holographic recipe to reconstruct α' corrections to anti-de Sitter (AdS) (quantum) gravity from an underlying CFT in the strictly planar limit (N → ∞). Assuming that the boundary CFT can be solved in principle to all orders of the 't Hooft coupling λ, for scalar primary operators, the λ - 1 expansion of the conformal dimensions can be mapped to higher curvature corrections of the dual bulk scalar field action. Furthermore, for the metric perturbations in the bulk, the AdS / CFT operator-field isomorphism forces these corrections to be of the Lovelock type. We demonstrate this by reconstructing the coefficient of the leading Lovelock correction, also known as the Gauss-Bonnet term in a bulk AdS gravity action using the expression of stress-tensor two-point function up to subleading order in λ - 1. [ABSTRACT FROM AUTHOR]