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Condensed matter physics, area laws & LQG?

  1. Aug 9, 2016 #341

    haushofer

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    I'm not sure whether this is the right topic, but here goes my question:

    Recently I stumbled upon the so-called Tsallis entropy (a nice discussion is given by http://iopscience.iop.org/article/10.1088/2058-7058/27/05/39/pdf). This is a generalized notion of entropy, which in a certain limit (no correlation between subsystems) reduces to the Boltzmann-Gibbs entropy, similar to how the limit v/c --> 0 of special relativity reduces to Galilean relativity.

    How is this reconcilable with holography? Holography is greatly motivated by the non-extensive nature of black hole entropy. Any thoughts?
     
  2. Aug 10, 2016 #342

    atyy

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    http://arxiv.org/abs/1608.02932
    Holographic relations in loop quantum gravity
    Lee Smolin
    (Submitted on 9 Aug 2016)
    It is shown that a relation between entropy and minimal area holds in loop quantum gravity, reminiscent of the Ryu-Takayanagi relation.
     
  3. Aug 10, 2016 #343

    atyy

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    I haven't seen anything about the Tsallis entropy in the holographic literature, but another generalization of the Boltzmann-Gibbs-Shannon-von Neumann entropy is the Renyi entropy, and there have been papers on these and holography, eg. http://arxiv.org/abs/1006.0047, https://arxiv.org/abs/1110.1084, https://arxiv.org/abs/1306.4682.

    I guess that may be because the BGS entropy needs von Neumann's generalization for quantum entanglement, and I'm not sure what the quantum generalization of the Tsallis entropy would be.
     
  4. Aug 10, 2016 #344

    haushofer

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    Apparently this notion of Tsallis entropy is big business in the stat.mech. field, but I cannot find a decent theoretical justification for it other than "let's keep entropy extensive in all cases". The Renyi entropy sounds familiar from the "spacetime is due to quantum entanglement of the vacuum"-claims. Anyway, thanks for your insight and papers!
     
  5. Aug 10, 2016 #345

    atyy

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    Yes, I looked at it many years ago, because many people use entropy measures in neuroscience. Interesting comments from Corfield in http://math.ucr.edu/home/baez/corfield/2006/06/tsallis-entropy.html, and from Baez in the comments section.
     
  6. Aug 19, 2016 #346

    atyy

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    http://arxiv.org/abs/1608.04744
    Zero Modes and Entanglement Entropy
    Yasaman K. Yazdi
    (Submitted on 16 Aug 2016)
    Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.

    http://arxiv.org/abs/1608.04900
    On the logarithmic divergent part of entanglement entropy, smooth versus singular regions
    Harald Dorn
    (Submitted on 17 Aug 2016)
    The entanglement entropy for smooth regions A has a logarithmic divergent contribution with a shape dependent coefficient and that for regions with conical singularities an additional log2 term. Comparing the coefficient of this extra term, obtained by direct holographic calculation for an infinite cone, with the corresponding limiting case for the shape dependent coefficient for a regularised cone, a mismatch by a factor two has been observed in the literature. We discuss several aspects of this issue. In particular a regularisation of A, intrinsically delivered by the holographic picture, is proposed and applied to an example of a compact region with two conical singularities. Finally, the mismatch is removed in all studied regularisations of A, if equal scale ratios are chosen for the limiting procedure.

    http://arxiv.org/abs/1608.04948
    TASI lectures on AdS/CFT
    Joao Penedones
    (Submitted on 17 Aug 2016)
    We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of the main properties of Mellin amplitudes for CFT correlation functions and their uses in the context of AdS/CFT.
    http://arxiv.org/abs/1608.05090
    Matrix Quantum Mechanics from Qubits
    Sean A. Hartnoll, Liza Huijse, Edward A. Mazenc
    (Submitted on 17 Aug 2016)
    We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O(N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1+1 dimensional spacetime.
     
    Last edited: Aug 24, 2016
  7. Aug 29, 2016 #347

    atyy

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    http://arxiv.org/abs/1608.07473
    From physical symmetries to emergent gauge symmetries
    Carlos Barceló, Raúl Carballo-Rubio, Francesco Di Filippo, Luis J. Garay
    (Submitted on 26 Aug 2016)
    Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
     
  8. Aug 31, 2016 #348

    atyy

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    http://arxiv.org/abs/1608.08695
    Broken bridges: A counter-example of the ER=EPR conjecture
    Pisin Chen, Chih-Hung Wu, Dong-han Yeom
    (Submitted on 31 Aug 2016)
    In this paper, we provide a counter-example to the ER=EPR conjecture. In an anti-de Sitter space, we construct a pair of maximally entangled but separated black holes. Due to the vacuum decay of the anti-de Sitter background toward a deeper vacuum, these two parts can be trapped by bubbles. If these bubbles are reasonably large, then within the scrambling time, there should appear an Einstein-Rosen bridge between the two black holes. Now by tracing more details on the bubble dynamics, one can identify parameters such that one of the two bubbles either monotonically shrinks or expands. Because of the change of vacuum energy, one side of the black hole would evaporate completely. Due to the shrinking of the apparent horizon, a signal of one side of the Einstein-Rosen bridge can be viewed from the opposite side. We analytically and numerically demonstrate that within a reasonable semi-classical parameter regime, such process can happen. Therefore, the ER=EPR conjecture cannot be generic in its present form and its validity maybe restricted.
     
  9. Sep 2, 2016 #349

    atyy

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    http://arxiv.org/abs/1609.00207
    Gravitational action with null boundaries
    Luis Lehner, Robert C. Myers, Eric Poisson, Rafael D. Sorkin
    (Submitted on 1 Sep 2016)
    We present a complete discussion of the boundary term in the action functional of general relativity when the boundary includes null segments in addition to the more usual timelike and spacelike segments. We confirm that ambiguities appear in the contribution from a null segment, because it depends on an arbitrary choice of parametrization for the generators. We also show that similar ambiguities appear in the contribution from a codimension-two surface at which a null segment is joined to another (spacelike, timelike, or null) segment. The parametrization ambiguity can be tamed by insisting that the null generators be affinely parametrized; this forces each null contribution to the boundary action to vanish, but leaves intact the fredom to rescale the affine parameter by a constant factor on each generator. Once a choice of parametrization is made, the ambiguity in the joint contributions can be eliminated by formulating well-motivated rules that ensure the additivity of the gravitational action. Enforcing these rules, we calculate the time rate of change of the action when it is evaluated for a so-called "Wheeler-deWitt patch" of a black hole in asymptotically-anti de Sitter space. We recover a number of results cited in the literature, obtained with a less complete analysis.

    http://arxiv.org/abs/1609.00026
    Lectures on Gravity and Entanglement
    Mark Van Raamsdonk
    (Submitted on 31 Aug 2016)
    The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered fascinating connections between quantum information theory and quantum gravity, suggesting that spacetime geometry is directly related to the entanglement structure of the underlying quantum mechanical degrees of freedom and that aspects of spacetime dynamics (gravitation) can be understood from basic quantum information theoretic constraints. In these notes, we provide an elementary introduction to these developments, suitable for readers with some background in general relativity and quantum field theory. The notes are based on lectures given at the CERN Spring School 2014, the Jerusalem Winter School 2014, the TASI Summer School 2015, and the Trieste Spring School 2015.
     
  10. Sep 6, 2016 #350

    atyy

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    http://arxiv.org/abs/1609.01287
    Holographic Entanglement Entropy
    Mukund Rangamani, Tadashi Takayanagi
    (Submitted on 5 Sep 2016)
    We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map.
    This is a preliminary draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application of holographic ideas to computation of entanglement entropy in strongly coupled field theories, and discussion of tensor networks and holography, which we have chosen to exclude from the current manuscript.
     
  11. Sep 14, 2016 #351

    atyy

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    http://arxiv.org/abs/1609.03560
    Classical Holographic Codes
    Enrico M. Brehm, Benedikt Richter
    (Submitted on 12 Sep 2016)
    In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.

    http://arxiv.org/abs/1609.03651
    Discussion of the Entanglement Entropy in Quantum Gravity
    Chen-Te Ma
    (Submitted on 13 Sep 2016)
    Quantum gravity needs to be satisfied by the holographic principle, and the entanglement entropy already has holographic evidences via anti-de Sitter/ Conformal field theory correspondence. Thus, we explore principles of quantum gravity via the entanglement entropy. We compute the entanglement entropy in two dimensional Einstein-Hilbert action to understand quantum geometry and area law. Then we also discuss two dimensional conformal field theory because we expect strongly coupled conformal field theory can describe perturbative quantum gravity theory. We find universal terms of the entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval and some cases of multiple intervals. To extend our discussion to generic multiple intervals, we use a geometric method to determine the entanglement entropy. Finally, we argue translational invariance possibly be a necessary condition in quantum gravity theory from ruing out volume law of the entanglement entropy.

    http://arxiv.org/abs/1609.03991
    Entwinement in discretely gauged theories
    V. Balasubramanian, A. Bernamonti, B. Craps, T. De Jonckheere, F. Galli
    (Submitted on 13 Sep 2016)
    We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an ##S_{N}## gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to ##AdS_{3}## at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M=0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.
     
  12. Sep 14, 2016 #352

    atyy

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    http://arxiv.org/abs/1609.04036
    The Black Hole Information Problem
    Joseph Polchinski
    (Submitted on 13 Sep 2016)
    The black hole information problem has been a challenge since Hawking's original 1975 paper. It led to the discovery of AdS/CFT, which gave a partial resolution of the paradox. However, recent developments, in particular the firewall puzzle, show that there is much that we do not understand. I review the black hole, Hawking radiation, and the Page curve, and the classic form of the paradox. I discuss AdS/CFT as a partial resolution. I then discuss black hole complementarity and its limitations, leading to many proposals for different kinds of `drama.' I conclude with some recent ideas.
     
  13. Sep 16, 2016 #353

    atyy

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    http://arxiv.org/abs/1609.04645
    From Path Integrals to Tensor Networks for AdS/CFT
    Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe
    (Submitted on 15 Sep 2016)
    In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient optimization by making its UV cut off position dependent and define a quantum state at each length scale. We conjecture that this path-integral corresponds to a time slice of AdS. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual 2d CFT. Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous MERA (cMERA). We also give a heuristic argument why we can expect a sub-AdS scale bulk locality for holographic CFTs.

    http://arxiv.org/abs/1609.04806
    On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
    Clement Delcamp, Bianca Dittrich, Aldo Riello
    (Submitted on 15 Sep 2016)
    Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non--Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non--Abelian analogue of the `magnetic centre choice', as obtained through an extended--Hilbert--space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement theory can be related to a choice of (squeezed) vacuum state.
     
  14. Sep 20, 2016 #354

    atyy

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    http://arxiv.org/abs/1609.05222
    What prevents gravitational collapse in string theory?
    Samir D. Mathur
    (Submitted on 16 Sep 2016)
    It is conventionally believed that if a ball of matter of mass M has a radius close to 2GM then it must collapse to a black hole. But string theory microstates (fuzzballs) have no horizon or singularity, and they do {\it not} collapse. We consider two simple examples from classical gravity to illustrate how this violation of our intuition happens. In each case the `matter' arises from an extra compact dimension, but the topology of this extra dimension is not trivial. The pressure and density of this matter diverge at various points, but this is only an artifact of dimensional reduction; thus we bypass results like Buchadahl's theorem. Such microstates give the entropy of black holes, so these topologically nontrivial constructions dominate the state space of quantum gravity.
     
  15. Sep 22, 2016 #355

    atyy

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    http://arxiv.org/abs/1609.06439
    Invitation to random tensors
    Razvan Gurau
    (Submitted on 21 Sep 2016)
    Preface to the SIGMA special issue "Tensor Models, Formalism and Applications." The SIGMA special issue "Tensor Models, Formalism and Applications" is a collection of eight excellent, up to date reviews \cite{Ryan:2016sundry,Bonzom:2016dwy,Rivasseau:2016zco,Carrozza:2016vsq,Krajewski:2016svb,Rivasseau:2016rgt,Tanasa:2015uhr,Gielen:2016dss} on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field.
    This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
     
  16. Oct 5, 2016 #356

    atyy

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    https://arxiv.org/abs/1610.00669
    Bulk Locality and Entanglement Swapping in AdS/CFT
    William R. Kelly
    (Submitted on 3 Oct 2016)
    Localized bulk excitations in AdS/CFT are produced by operators which modify the pattern of entanglement in the boundary state. We show that simple models--consisting of entanglement swapping operators acting on a qubit system or a free field theory--capture qualitative features of gravitational backreaction and reproduce predictions of the Ryu-Takayanagi formula. These entanglement swapping operators naturally admit multiple representations associated with different degrees of freedom, thereby reproducing the code subspace structure emphasized by Almheiri, Dong, and Harlow. We also show that the boundary Reeh-Schlieder theorem implies that equivalence of certain operators on a code subspace necessarily breaks down when non-perturbative effects are taken into account (as is expected based on bulk arguments).
     
  17. Oct 7, 2016 #357

    atyy

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    https://arxiv.org/abs/1610.01719
    Entanglement in a two-dimensional string theory
    William Donnelly, Gabriel Wong
    (Submitted on 6 Oct 2016)
    What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider entanglement entropy in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large ##N##. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space, giving a precise state-counting interpretation to the entropy, including its leading ##O(N^{2})## piece. In the process we reinterpret the sphere partition function as a thermal ensemble of of open strings whose endpoints are anchored to an object at the entangling surface that we call an E-brane.
     
  18. Oct 28, 2016 #358

    atyy

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    https://arxiv.org/abs/1610.08516
    Into the Bulk: A Covariant Approach
    Netta Engelhardt
    (Submitted on 26 Oct 2016)
    I propose a general, covariant way of defining when one region is "deeper in the bulk" than another. This definition is formulated outside of an event horizon (or in the absence thereof) in generic geometries; it may be applied to both points and surfaces, and may be used to compare the depth of bulk points or surfaces relative to a particular boundary subregion or relative to the entire boundary. Using the recently proposed "lightcone cut" formalism, the comparative depth between two bulk points can be determined from the singularity structure of Lorentzian correlators in the dual field theory. I prove that, by this definition, causal wedges of progressively larger regions probe monotonically deeper in the bulk. The definition furthermore matches expectations in pure AdS and in static AdS black holes with isotropic spatial slices, where a well-defined holographic coordinate exists. In terms of holographic RG flow, this new definition of bulk depth makes contact with coarse-graining over both large distances and long time scales.

    https://arxiv.org/abs/1610.08970
    Boundary Fluctuations and A Reduction Entropy
    Christopher Herzog, Kuo-Wei Huang
    (Submitted on 27 Oct 2016)
    The boundary Weyl anomalies live on a codimension-1 boundary, ∂M. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, Σ. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on ∂M to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.
     
  19. Nov 8, 2016 #359

    atyy

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    https://arxiv.org/abs/1611.02647
    Multipartite Entanglement and Firewalls
    Shengqiao Luo, Henry Stoltenberg, Andreas Albrecht
    (Submitted on 8 Nov 2016)
    Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a "firewall" inside the black hole horizon which prevents objects from falling smoothly toward the singularity. A fundamental limitation on the behavior of quantum entanglement known as "monogamy" plays a key role in the AMPS argument. Our goal is to study and apply many-body entanglement theory to consider the entanglement among different parts of Hawking radiation and black holes. Using the multipartite entanglement measure called negativity, we identify an example which could change the AMPS accounting of quantum entanglement and perhaps eliminate the need for a firewall. Specifically, we constructed a toy model for black hole decay which has different entanglement behavior than that assumed by AMPS. We discuss the additional steps that would be needed to bring lessons from our toy model to our understanding of realistic black holes.
     
  20. Nov 10, 2016 #360

    atyy

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    https://arxiv.org/abs/1611.02702
    Toward a Holographic Theory for General Spacetimes
    Yasunori Nomura, Nico Salzetta, Fabio Sanches, Sean J. Weinberg
    (Submitted on 8 Nov 2016)
    We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct sum and "spacetime equals entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.
     
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