The origin of the AdS/CFT correspondence is from the description of D-branes in open and closed string theory, and is a consequence of open-closed string duality (see for a very accessible account). with constant negative curvature near the boundary) and a (super)conformal gauge theory. The AdS/CFT correspondence is a concrete instance of a holographic duality between quantum (super)gravity with asymptotically anti-de Sitter ( AdS) boundary conditions (i.e. More precise versions of this argument incorporating covariance under diffeomorphisms and inputs from quantum information theory have been instrumental in providing a concrete ground for the holographic principle which states that a quantum theory of gravity in a spacetime with appropriate asymptotic boundary conditions can be described in terms of a (non-gravitational) quantum many-body system living at the boundary. This heuristic argument relies on a semi-classical description of gravity and should be approximately correct if the size of the box is very large so that gravity is weak even at the black hole horizon when the black hole is of the same size as the box. the quarter of the area A of the horizon measured in Planck units (we set \(\hbar = c =1\)). The maximal entropy of a theory of gravity inside the box would then be the Bekenstein–Hawking entropy of the black hole whose horizon is of the size of the box, which explicitly is A/4 G, i.e. The heuristic reasoning for the holographic principle of gravity is simply that if we stuff in enough matter in a box, then eventually it will collapse to form a black hole whose maximum possible size would be that of the box. The AdS/CFT correspondence is the most well understood example of the holographic emergence of spacetime and gravity. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. The importance of understanding the modular flow in the dual field theory has been emphasized. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes.
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