General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. In the context of the AdS/CFT correspondence, we study several holographic probes that relate information about the bulk spacetime to CFT data. The best-known example is the relation between minimal surfaces in the bulk and entanglement entropy of a subregion in the CFT. Building on earlier work, we identify "shadows" in the bulk: regions that are not illuminated by any of the bulk probes we consider, in the sense that the bulk surfaces do not pass through these regions. We quantify the size of the shadow in the near-horizon region of a black hole and in the vicinity of a sufficiently dense star. The existence of shadows motivates further study of the bulk-boundary dictionary in order to identify CFT quantities that encode information about the shadow regions in the bulk. We speculate on the interpretation of our results from a dual field theory perspective.

A puzzling aspect of the AdS/CFT correspondence is that a single bulk operator can be mapped to multiple different boundary operators, or precursors. By improving upon a recent model of Mintun, Polchinski, and Rosenhaus, we demonstrate explicitly how this ambiguity arises in a simple model of the field theory. In particular, we show how gauge invariance in the boundary theory manifests as a freedom in the smearing function used in the bulk-boundary mapping, and explicitly show how this freedom can be used to localize the precursor in different spatial regions. We also show how the ambiguity can be understood in terms of quantum error correction, by appealing to the entanglement present in the CFT. The concordance of these two approaches suggests that gauge invariance and entanglement in the boundary field theory are intimately connected to the reconstruction of local operators in the dual spacetime.

We investigate sub-AdS scale locality in a weakly coupled toy model of the AdS 3 /CFT 2 correspondence. We find that this simple model has the correct density of states at low and high energies to be dual to Einstein gravity coupled to matter in AdS 3 . The bulk correlation functions also have the correct behavior at leading order in the large N expansion, but non-local effects emerge at order 1/N . Our analysis leads to the conjecture that any large N CFT 2 that is both modular invariant, and exhibits the correct low-energy density of states, is dual to a gravitational theory with sub-AdS scale locality.

The firewall paradox states that an observer falling into an old black hole must see a violation of unitarity, locality, or the equivalence principle. Motivated by this remarkable conflict, we analyze the causal structure of black hole spacetimes in order to determine whether all the necessary ingredients for the paradox fit within a single observer's causal patch. We particularly focus on the question of whether the interior partner modes of the outgoing Hawking quanta can, in principle, be measured by an infalling observer. Since the relevant modes are spread over the entire sphere, we answer a simple geometrical question: can any observer see an entire sphere behind the horizon? We find that for all static black holes in 3 þ 1 and higher dimensions, with any value of the cosmological constant, no single observer can see both the early Hawking radiation and the interior modes with low angular momentum. We present a detailed description of the causal patch geometry of the Schwarzschild black hole in 3 þ 1 dimensions, where an infalling observer comes closest to being able to measure the relevant modes.

Abstract:We study the power-and bi-spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one-parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch-Davies vacuum state. Selecting the Bunch-Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch-Davies state the hyperbolic de Sitter n-point correlation functions have to match the planar de Sitter n-point correlation functions. The expressions for the planar and hyperbolic Bunch-Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power-and bi-spectrum. For the bi-spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch-Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.