Condensed matter physics, area laws & LQG?

[atyy]

http://arxiv.org/abs/1406.7304
Entanglement entropy and nonabelian gauge symmetry
William Donnelly
(Submitted on 27 Jun 2014)
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.

http://arxiv.org/abs/1406.7677
Evolution of Holographic n-partite Information
Mohsen Alishahiha, M. Reza Mohammadi Mozaffar, Mohammad Reza Tanhayi
(Submitted on 30 Jun 2014)
We study various scaling behaviors of n-partite information during a process of thermalization after a global quantum quench for n disjoint system consisting of n parallel strips whose widths are much larger than the separation between them. By making use of the holographic description for entanglement entropy we explore holographic description of the n-partite information by which we show that it has a definite sign: it is positive for even n and negative for odd n. This might be thought of as an intrinsic property of a field theory which has gravity dual.

 

[atyy]

http://arxiv.org/abs/1407.0284
The Tensor Theory Space
Vincent Rivasseau
(Submitted on 1 Jul 2014)
The tensor track is a background-independent discretization of quantum gravity which includes a sum over all topologies. We discuss how to define a functional renormalization group flow and the Wetterich equation in the corresponding theory space. This space is different from the Einsteinian theory space of asymptotic safety. It includes all fixed-rank tensor-invariant interactions, hence generalizes matrix models and the (Moyal) non-commutative field theory space.

 

[atyy]

http://arxiv.org/abs/1407.1855
Kenneth G. Wilson: Renormalized After-Dinner Anecdotes
Paul Ginsparg
(Submitted on 7 Jul 2014)
This is the transcript of the after-dinner talk I gave at the close of the 16 Nov 2013 symposium "Celebrating the Science of Kenneth Geddes Wilson" [1] at Cornell University (see Fig. 1 for the poster). The video of my talk is on-line [2], and this transcript is more or less verbatim, with the slides used included as figures. I've also annotated it with a few clarifying footnotes, and provided references to the source materials where available.
The talk itself pulls together anecdotes from various points in his career, discusses my own graduate student experiences with him, and finishes with some video excerpts from an interview he did in 2010.

http://www.physics.cornell.edu/events-2/ken-wilson-symposium/ken-wilson-symposium-videos/
Ken Wilson Symposium – Videos
November 16, 2013
1. David Mermin, Cornell University – “Early Memories of Ken”
2. Peter Lepage, Cornell University – “Ken Wilson and Lattice QCD”
3. Michael Peskin, SLAC – “Ken Wilson: Solving the Strong Interactions”
4. Benjamin Widom, Cornell University – “Talking Science with Kenneth Wilson at Cornell”
5. David Gross, Santa Barbara – “Quantum Field Theory – Then and Now”
6. Edouard Brezin, ENS Paris – “A Paradigmatic Shift”
7. Steve White, Irvine – “Ken Wilson and Quantum Chemistry”
8. Open Mic
9. Paul Ginsparg, Cornell University – After Dinner Talk

 

[marcus]

http://arxiv.org/abs/1407.2658
Reconstructing quantum states from local data
Brian Swingle, Isaac H. Kim
(Submitted on 10 Jul 2014)
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximal global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed by taking the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate subspace of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We show that perfect local reconstruction is also possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy", and we discuss its relation to emergent geometry in the context of holographic duality.
4+2 pages

 

[atyy]

http://arxiv.org/abs/1407.4467
When UV and IR Collide: Inequivalent CFTs From Different Foliations Of AdS
Borun D. Chowdhury, Maulik K. Parikh
(Submitted on 16 Jul 2014)
In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincar\'e coordinates for AdS3. We refer to these as global-CFT, Rindler-CFT and Poincar\'e-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS3, we discuss the implications of our results for bulk duals of periodically-identified Poincar\'e and Rindler-CFTs. Our results are consistent with some recent proposals suggesting a modification of the semi-classical BTZ geometry close to the horizons.

http://arxiv.org/abs/1407.4615
Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
Sylvain Carrozza
(Submitted on 17 Jul 2014)
This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the gauge group SU(2), and as such is expected to be related to Euclidean quantum gravity in three dimensions. By means of a power-counting argument, we introduce a notion of dimensionality of the free parameters defining the action. General flow equations for the dimensionless bare coupling constants can then be derived, in terms of a discretely varying cut-off, and in which all the so-called melonic Feynman diagrams contribute. Linearizing around the Gaussian fixed point allows to recover the splitting between relevant, irrelevant, and marginal coupling constants. Pushing the perturbative expansion to second order for the marginal parameters, we are able to determine their behaviour in the vicinity of the Gaussian fixed point. Along the way, several technical tools are reviewed, including a discussion of combinatorial factors and of the Laplace approximation, which reduces the evaluation of the amplitudes in the UV limit to that of Gaussian integrals.

 

[atyy]

http://arxiv.org/abs/1407.5629
Entanglement entropy of Wilson loops: Holography and matrix models
Simon A. Gentle, Michael Gutperle
(Submitted on 21 Jul 2014)
A half-BPS circular Wilson loop in $\mathcal{N}=4$ $SU(N)$ supersymmetric Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this note we utilize the supergravity solutions that are dual to such Wilson loops in a representation with order $N^{2}$ boxes to calculate this entropy holographically. Employing the matrix model results of Gomis, Matsuura, Okuda and Trancanelli we express this holographic entanglement entropy in a form that can be compared with the calculation of Lewkowycz and Maldacena. We find complete agreement between the matrix model and holographic calculations.

 

[atyy]

http://arxiv.org/abs/1407.6532
Electromagnetism as an emergent phenomenon: a step-by-step guide
Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay, Gil Jannes
(Submitted on 24 Jul 2014)
We give a detailed description of Electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two scenarios that, although qualitatively different, share some important features, with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Maxwell's mechanical model for Electrodynamics, where Maxwell's equations appear as dynamical consistency conditions. We next take a superfluid 3He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and that it is only in the low-energy regime that this physical reality is blurred in favour of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance.

http://arxiv.org/abs/1407.6552
Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
Roman Orus
(Submitted on 24 Jul 2014)
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from Projected Entangled Pair States (PEPS), and the relation between the Multi-scale Entanglement Renormalization Ansatz (MERA) and the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement in the emergence of several physical properties and objects through the TN language. Some recent results along these lines are also discussed.

 

[atyy]

http://arxiv.org/abs/1407.7746
On background-independent renormalization of spin foam models
Benjamin Bahr
(Submitted on 29 Jul 2014)
In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical consistency of path integral measures gives a natural analogue of Wilson's RG flow equations for background-independent systems. We discuss the conditions for the continuum measures to be diffeomorphism-invariant, and consider both exact and approximate examples.

 

[atyy]

http://arxiv.org/abs/1407.8273
Holographic Entropy Production
Yu Tian, Xiao-Ning Wu, Hong-Bao Zhang
(Submitted on 31 Jul 2014)
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalization is explained.

http://arxiv.org/abs/1407.8203
Renormalization group constructions of topological quantum liquids and beyond
Brian Swingle, John McGreevy
(Submitted on 30 Jul 2014)
We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective. We report four main results. First, we argue for the "weak area law": any gapped phase with a unique ground state on every closed manifold obeys the area law. Second, we introduce an RG based classification scheme and give a detailed argument that all phases within the classification scheme obey the area law. Third, we define a special sub-class of gapped phases, topological quantum liquids, which captures all examples of current physical relevance, and we rigorously show that TQLs obey an area law. Fourth, we show that all topological quantum liquids have MERA representations which achieve unit overlap with the ground state in the thermodynamic limit and which have a bond dimension scaling with system size L as $e^{clog^{d(1+δ)}(L)}$ for all $δ>0$. For example, we show that chiral phases in d=2 dimensions have an approximate MERA with bond dimension $e^{clog^{2(1+δ)}(L)}$. We discuss extensively a number of subsidiary ideas and results necessary to make the main arguments, including field theory constructions. While our argument for the general area law rests on physically-motived assumptions (which we make explicit) and is therefore not rigorous, we may conclude that "conventional" gapped phases obey the area law and that any gapped phase which violates the area law must be a dragon.

http://arxiv.org/abs/1202.1695
Spin-spin correlations of entangled qubit pairs in the Bohm interpretation of quantum mechanics
A. Ramsak
(Submitted on 8 Feb 2012)
A general entangled qubit pair is analyzed in the de Broglie-Bohm formalism corresponding to two spin-1/2 quantum rotors. Several spin-spin correlators of Bohm's hidden variables are analyzed numerically and a detailed comparison with results obtained by standard quantum mechanics is outlined. In addition to various expectation values the Bohm interpretation allows also a study of the corresponding probability distributions, which enables a novel understanding of entangled qubit dynamics. In particular, it is shown how the angular momenta of two qubits in this formalism can be viewed geometrically and characterized by their relative angles. For perfectly entangled pairs, for example, a compelling picture is given, where the qubits exhibit a unison precession making a constant angle between their angular momenta. It is also demonstrated that the properties of standard quantum mechanical spin-spin correlators responsible for the violation of Bell's inequalities are identical to their counterparts emerging from the probability distributions obtained by the Bohmian approach.

 

[atyy]

http://arxiv.org/abs/1408.0121
Thermally correlated states in Loop Quantum Gravity
Goffredo Chirco, Carlo Rovelli, Paola Ruggiero
(Submitted on 1 Aug 2014)
We study a class of loop-quantum-gravity states characterized by (ultra-local) thermal correlations that reproduce some features of the ultraviolet structure of the perturbative quantum field theory vacuum. In particular, they satisfy an analog of the Bisognano-Wichmann theorem. These states are peaked on the intrinsic geometry and admit a semiclassical interpretation. We study how the correlations extend on the spin-network beyond the ultra local limit.

marcus has started a discussion on this paper: https://www.physicsforums.com/showthread.php?t=764628

 

[atyy]

http://arxiv.org/abs/1408.3203
Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
Netta Engelhardt, Aron C. Wall
(Submitted on 14 Aug 2014)
We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.

 

[marcus]

http://arxiv.org/abs/1408.3705
Deriving the First Law of Black Hole Thermodynamics without Entanglement
William R. Kelly
(Submitted on 16 Aug 2014)
In AdS/CFT, how is the bulk first law realized in the boundary CFT? Recently, Faulkner et al. showed that in certain holographic contexts, the bulk first law has a precise microscopic interpretation as a first law of entanglement entropy in the boundary theory. However, the bulk can also satisfy a first law when the boundary density matrix is pure, i.e. in the absence of entanglement with other degrees of freedom. In this note we argue that the bulk first law should generally be understood in terms of a particular coarse-graining of the boundary theory. We use geons, or single-exterior black holes, as a testing ground for this idea. Our main result is that for a class of small perturbations to these spacetimes the Wald entropy agrees to first order with the one-point entropy, a coarse-grained entropy recently proposed by Kelly and Wall. This result also extends the regime over which the one-point entropy is known to be equal to the causal holographic information of Hubeny and Rangamani.
18 pages, 2 figures

This looked interesting and I thought it might fit in with this biblio thread. W.R.Kelly is a young researchers at Santa Barbara who has co-authored a couple of times with Don Marolf and a couple of times with Aron C. Wall (see atty's preceding post).

This might also be of interest to people following this biblio thread:
http://arxiv.org/abs/1408.3989
Observing Shape in Spacetime
Sean Gryb
(Submitted on 18 Aug 2014)
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms - namely hypersurface deformations - are, in a certain sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of "Shape Observer" that represents a conformal reference frame that is dual to the notion of inertial reference frame in spacetime. We then provide a precise dictionary relating the two notions. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.
23 pages, 3 figures.

 

[atyy]

http://arxiv.org/abs/1408.4770
Holographic Holes and Differential Entropy
Matthew Headrick, Robert C. Myers, Jason Wien
(Submitted on 20 Aug 2014)
Recently, it has been shown by Balasubramanian et al. and Myers et al. that the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in the bulk of a holographic spacetime has an interpretation as the differential entropy of a particular family of intervals (or strips) in the boundary theory. We first extend this construction to bulk surfaces which vary in time. We then give a general proof of the equality between the gravitational entropy and the differential entropy. This proof applies to a broad class of holographic backgrounds possessing a generalized planar symmetry and to certain classes of higher-curvature theories of gravity. To apply this theorem, one can begin with a bulk surface and determine the appropriate family of boundary intervals by considering extremal surfaces tangent to the given surface in the bulk. Alternatively, one can begin with a family of boundary intervals; as we show, the differential entropy then equals the gravitational entropy of a bulk surface that emerges from the intersection of the neighboring entanglement wedges, in a continuum limit.

 

[atyy]

http://arxiv.org/abs/1408.5179
No Firewalls for Black Holes Entangled with Large Systems
Henry Stoltenberg, Andreas Albrecht
(Submitted on 22 Aug 2014)
We question the idea that firewalls are a typical feature of black holes. We first review the arguments of AMPS favoring firewalls, focusing on entanglements in a simple toy model for a black hole and the Hawking radiation. By introducing a large and inaccessible system (representing perhaps a de Sitter stretched horizon or inaccessible part of a landscape) we show complementarity can be restored and firewalls can be avoided throughout the black hole's evolution. We also argue that under these conditions black holes do not have an "information problem".

 

[atyy]

http://arxiv.org/abs/1408.5589
Derivation of Gravitational Field Equation from Entanglement Entropy
Hiroaki Matsueda
(Submitted on 24 Aug 2014)
In this paper, I am going to reformulate my previous work on emergent general relativity from quantum information metric (arXiv:1310.1831) so that we can relate it with some other results based on the entropy-energy relation. For this purpose, I propose a new equality that the second derivative of the entanglement entropy directly represents the spacetime metric. Then, we derive the Einstein tensor from the metric, and consider the meaning of emergent energy-momentum tensor. I demonstrate an explicite example based on spatially one-dimensional quantum states near criticality. I also comment on close connection of the present approach with the Ryu-Takayanagi formula.

 

[atyy]

http://arxiv.org/abs/1408.6005
A Holographic Approach to Spacetime Entanglement
Jason Wien
An essay presented to the Perimeter Institute for the completion of Perimeter Scholars International and the requirements for the degree of Master of Science
(Submitted on 26 Aug 2014)
Recently it has been proposed that the Bekenstein-Hawking formula for the entropy of spacetime horizons has a larger significance as the leading contribution to the entanglement entropy of general spacetime regions, in the underlying quantum theory [2]. This `spacetime entanglement conjecture' has a holographic realization that equates the entropy formula evaluated on an arbitrary space-like co-dimension two surface with the differential entropy of a particular family of co-dimension two regions on the boundary. The differential entropy can be thought of as a directional derivative of entanglement entropy along a family of surfaces. This holographic relation was first studied in [3] and extended in [4], and it has been proven to hold in Einstein gravity for bulk surfaces with planar symmetry (as well as for certain higher curvature theories) in [4]. In this essay, we review this proof and provide explicit examples of how to build the appropriate family of boundary intervals for a given bulk curve. Conversely, given a family of boundary intervals, we provide a method for constructing the corresponding bulk curve in terms of intersections of entanglement wedge boundaries. We work mainly in three dimensions, and comment on how the constructions extend to higher dimensions.

 

[atyy]

http://arxiv.org/abs/1408.6300
Causality & holographic entanglement entropy
Matthew Headrick, Veronika E. Hubeny, Albion Lawrence, Mukund Rangamani
(Submitted on 27 Aug 2014)
We identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.

 

[atyy]

http://arxiv.org/abs/1408.6633
Geodesic Distance in Fisher Information Space and Holographic Entropy Formula
Hiroaki Matsueda
(Submitted on 28 Aug 2014)
In this short note, we examine geodesic distance in Fisher information space in which the metric is defined by the entanglement entropy in CFT_(1+1). It is obvious in this case that the geodesic distance at a constant time is a function of the entropy data embedded into the information space. In a special case, the geodesic equation can be solved analytically, and we find that the distance agrees well with the Ryu-Takayanagi formula. Then, we can understand how the distance looks at the embeded quantum information. The result suggests that the Fisher metric is an efficient tool for constructing the holographic spacetime.

 

[friend]

http://arxiv.org/abs/1408.6633
Geodesic Distance in Fisher Information Space and Holographic Entropy Formula

It sounds here as if the author has connected GR to QM. That would be amazing, right?

 

[atyy]

Posted by marcus in his bibliography https://www.physicsforums.com/showpost.php?p=4839015&postcount=2240

http://arxiv.org/abs/1409.0144
Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
Eugenio Bianchi, Tommaso De Lorenzo, Matteo Smerlak
(Submitted on 30 Aug 2014)
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that (i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, (ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, (iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

 

[atyy]

It sounds here as if the author has connected GR to QM. That would be amazing, right?

Yes, it would be amazing. Here is a slightly earlier paper by Matsueda http://arxiv.org/abs/1408.5589 which proposes a way to extend the results of Blanco et al http://arxiv.org/abs/1305.3182. Blanco's work was important, because it showed how within AdS/CFT which is already a proposal connecting QM and GR, one might understand the thermodynamic derivation of GR by Jacobson.

 

[atyy]

http://arxiv.org/abs/1409.1231
Jerusalem Lectures on Black Holes and Quantum Information
Daniel Harlow
(Submitted on 3 Sep 2014)
In these lectures I give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. I also give an introduction to holography and the AdS/CFT correspondence, focusing on those aspects which are relevant for the black hole information problem.

 

[atyy]

http://arxiv.org/abs/1409.1603
Non-Unitary Holography
Cumrun Vafa
(Submitted on 4 Sep 2014)
We propose gauge theory/gravity duality involving conformal theories based on U(N+k|k) gauge groups. We show that to all orders in 1/N these non-unitary theories based on supergroups are indistinguishable from the corresponding unitary theories where the gauge group is replaced by U(N). This leads to non-unitary gravity duals which to all orders in 1/N are indistinguishable from their unitary cousins. They are distinguished by operators whose correlation functions differ by O(exp(-aN)). The celebrated type IIB on AdS^5 x S^5 and M-theory on AdS^4 x S^7 fall in this class and thus seem to also admit non-unitary non-perturbative completions. It is tempting to conjecture that this setup may provide a non-unitary model for black hole evaporation.

 

[atyy]

http://arxiv.org/abs/1409.2407
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Bianca Dittrich, Sebastian Mizera, Sebastian Steinhaus
(Submitted on 8 Sep 2014)
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. Using this novel information encoded in the decoration might eventually lead to new methods incorporating both analytical and numerical techniques.

 

[atyy]

http://arxiv.org/abs/1409.3150
Group field theories for all loop quantum gravity
Daniele Oriti, James P. Ryan, Johannes Thürigen
(Submitted on 10 Sep 2014)
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the GFT formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

http://arxiv.org/abs/1409.3085
A Formulation of Lattice Gauge Theories for Quantum Simulations
Erez Zohar, Michele Burrello
(Submitted on 10 Sep 2014)
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete D3 gauge group, are presented.

 

[atyy]

I'm not entirely sure how this fits in, but one things I've been becoming aware of is that entanglement is relative. The entanglement entropy is absolute, in the sense that it is basis independent. However, here are some discussions that the notion of entanglement is relative.

http://arxiv.org/abs/quant-ph/0206135
Entanglement of photons
S.J. van Enk
(Submitted on 19 Jun 2002)
It is argued that the title of this paper represents a misconception. Contrary to widespread beliefs it is electromagnetic field modes that are "systems'' and can be entangled, not photons. The amount of entanglement in a given state is shown to depend on redefinitions of the modes; we calculate the minimum and maximum over all such redefinitions for several examples.

http://arxiv.org/abs/1302.3509
Universal Separability and Entanglement in Identical Particle Systems
Toshihiko Sasaki, Tsubasa Ichikawa, Izumi Tsutsui
(Submitted on 14 Feb 2013)
Entanglement is known to be a relative notion, defined with respect to the choice of physical observables to be measured (i.e., the measurement setup used). This implies that, in general, the same state can be both separable and entangled for different measurement setups, but this does not exclude the existence of states which are separable (or entangled) for all possible setups. We show that for systems of bosonic particles there indeed exist such universally separable states: they are i.i.d. pure states. In contrast, there is no such state for fermionic systems with a few exceptional cases. We also find that none of the fermionic and bosonic systems admits universally entangled states.

 

[marcus]

http://arxiv.org/abs/1409.8339
All-fermion electrodynamics and fermion number anomaly inflow
S. M. Kravec, John McGreevy, Brian Swingle
(Submitted on 29 Sep 2014)
We demonstrate that 3+1-dimensional quantum electrodynamics with fermionic charges, fermionic monopoles, and fermionic dyons arises at the edge of a 4+1-dimensional gapped state with short-range entanglement. This state cannot be adiabatically connected to a product state, even in the absence of any symmetry. This provides independent evidence for the obstruction found byarXiv:1306.3238 to a 3+1-dimensional short-distance completion of all-fermion electrodynamics. The non-triviality of the bulk is demonstrated by a novel fermion number anomaly.
37 pages, 5 figures
Although I can't reliably tell, this sounded to me as if it might be of interest to you and might fit into the context of this thread. Atyy, let me know if it does't fit and I'll be happy to delete.

 

[atyy]

Although I can't reliably tell, this sounded to me as if it might be of interest to you and might fit into the context of this thread. Atyy, let me know if it does't fit and I'll be happy to delete.

Thanks for posting the Kravec, McGreevy, and Swingle paper! I think it's good to cast the net widely and to post whatever we think is potentially interesting.

 

[atyy]

http://arxiv.org/abs/1410.1540
The Information Theoretic Interpretation of the Length of a Curve
Bartlomiej Czech, Patrick Hayden, Nima Lashkari, Brian Swingle
(Submitted on 6 Oct 2014)
In the context of holographic duality with AdS3 asymptotics, the Ryu-Takayanagi formula states that the entanglement entropy of a subregion is given by the length of a certain bulk geodesic. The entanglement entropy can be operationalized as the entanglement cost necessary to transmit the state of the subregion from one party to another while preserving all correlations with a reference party. The question then arises as to whether the lengths of other bulk curves can be interpreted as entanglement costs for some other information theoretic tasks. Building on recent results showing that the length of more general bulk curves is computed by the differential entropy, we introduce a new task called constrained state merging, whereby the state of the boundary subregion must be transmitted using operations restricted in location and scale in a way determined by the geometry of the bulk curve. Our main result is that the cost to transmit the state of a subregion under the conditions of constrained state merging is given by the differential entropy and hence the signed length of the corresponding bulk curve. When the cost is negative, constrained state merging distills entanglement rather than consuming it. This demonstration has two parts: first, we exhibit a protocol whose cost is the length of the curve and second, we prove that this protocol is optimal in that it uses the minimum amount of entanglement. In order to complete the proof, we additionally demonstrate that single-shot smooth conditional entropies for intervals in 1+1-dimensional conformal field theories with large central charge are well approximated by their von Neumann counterparts. We also revisit the relationship between the differential entropy and the maximum entropy among locally consistent density operators, demonstrating large quantitative discrepancy between the two quantities in conformal field theories.

 

[atyy]

http://arxiv.org/abs/1410.2870
Unravelling Holographic Entanglement Entropy in Higher Spin Theories
Alejandra Castro, Eva Llabrés
(Submitted on 10 Oct 2014)
There are two proposals that compute holographic entanglement entropy in AdS3 higher spin theories based on SL(N,R) Chern-Simons theory. We show explicitly that these two proposals are equivalent. We also designed two methods that solve systematically the equations for arbitrary N. For finite charge backgrounds in AdS3, we find exact agreement between our expressions and the short interval correction of the entanglement entropy for an excited state in a CFT2.

 

[atyy]

http://arxiv.org/abs/1410.7773
Large-N transitions of the connectivity index
Francesco Aprile, Vasilis Niarchos
(Submitted on 28 Oct 2014)
The connectivity index, defined as the number of decoupled components of a quantum system, can change under deformations of the Hamiltonian or during the dynamical change of the system under renormalization group flow. Such changes signal a rearrangement of correlations of different degrees of freedom across spacetime and field theory space. In this paper we quantify such processes by studying the behavior of entanglement entropy, relative quantum entropy and quantum mutual information in a specific example: the RG flow in the Coulomb branch of large-N superconformal field theories. We argue that in this context there is an interesting sharp large-N transition in the middle of the RG flow from a non-separable phase of the Higgsed UV gauge theory to a separable phase of deformed decoupled CFTs in the IR. The entanglement entropy on a sphere with radius ℓ detects this transition via the formation of a separatrix on the co-dimension-two Ryu-Takayanagi surface in multi-centered brane geometries above a critical value of ℓ. Other measures of entanglement and separability based on the relative quantum entropy detect a transition to a phase where they vanish identically. From the IR point of view the effect is closely related to the resummation of an infinite set of irrelevant multi-trace interactions.

 

[atyy]

http://arxiv.org/abs/1405.6394
Finite N and the failure of bulk locality: Black holes in AdS/CFT
Daniel Kabat, Gilad Lifschytz
(Submitted on 25 May 2014 (v1), last revised 20 Jul 2014 (this version, v2))
We consider bulk quantum fields in AdS/CFT in the background of an eternal black hole. We show that for black holes with finite entropy, correlation functions of semiclassical bulk operators close to the horizon deviate from their semiclassical value and are ill-defined inside the horizon. This is due to the large-time behavior of correlators in a unitary CFT, and means the region near and inside the horizon receives corrections. We give a prescription for modifying the definition of a bulk field in a black hole background, such that one can still define operators that mimic the inside of the horizon, but at the price of violating microcausality. For supergravity fields we find that commutators at spacelike separation generically ~ exp(-S/2). Similar results hold for stable black holes that form in collapse. The general lesson may be that a small amount of non-locality, even over arbitrarily large spacelike distances, is an essential aspect of non-perturbative quantum gravity.

http://arxiv.org/abs/1411.0690
Entanglement is not Enough
Leonard Susskind
(Submitted on 3 Nov 2014)
This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.

 

[atyy]

Reading Susskind's "Entanglenent is not enough", I see he and Stanford discussed tensor networks in these two papers:

http://arxiv.org/abs/1406.2678
Complexity and Shock Wave Geometries
Douglas Stanford, Leonard Susskind
(Submitted on 10 Jun 2014 (v1), last revised 12 Jun 2014 (this version, v2))
In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by GNlAdS. We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.

Edit: I deleted one reference, because I cut and pasted wrongly. The right paper is in the next post. Thanks, marcus!

 

[marcus]

Belongs with previous post:
http://arxiv.org/abs/1409.8180
Localized shocks
Daniel A. Roberts, Douglas Stanford, Leonard Susskind
(Submitted on 29 Sep 2014)
We study products of precursors of spatially local operators, W_xn(t_n)...W_x1(t₁), where W_x(t)=e^−iHtW_xe^iHt. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region that grows linearly in t. In a lattice system, products of such operators can be represented using tensor networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges supported by localized shock waves. We find a geometrical correspondence between these two descriptions, generalizing earlier work in the spatially homogeneous case.
23 pages plus appendices, 11 figures

 

[atyy]

The 2015 New Horizons in Physics Prizes

Sean Hartnoll, Stanford University, for applying holographic methods to obtain remarkable new insights into strongly interacting quantum matter.

Philip C. Schuster and Natalia Toro, Perimeter Institute, for pioneering the “simplified models” framework for new physics searches at the Large Hadron Collider, as well as spearheading new experimental searches for dark sectors using high-intensity electron beams.

Horacio Casini and Marina Huerta, CONICET and Instituto Balseiro, Universidad Nacional de Cuyo, Shinsei Ryu, University of Illinois at Urbana-Champaign, and Tadashi Takayanagi, Kyoto University, for fundamental ideas about entropy in quantum field theory and quantum gravity.

 

[atyy]

http://arxiv.org/abs/1411.7041
Bulk Locality and Quantum Error Correction in AdS/CFT
Ahmed Almheiri, Xi Dong, Daniel Harlow
(Submitted on 25 Nov 2014)
We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

 

[atyy]

http://simons.berkeley.edu/talks/brian-swingle-2014-04-22
Einstein's Equations Starting from Qubits
Brian Swingle, Harvard University

Part of the Tensor Networks and Simulations workshop, with lots of other good stuff at http://simons.berkeley.edu/workshops/schedule/81.

 

[marcus]

...good stuff at http://simons.berkeley.edu/workshops/schedule/81.
Including talks by Guifre Vidal and Xiao-Gang Wen : ^)

 

[atyy]

...good stuff at http://simons.berkeley.edu/workshops/schedule/81.
Including talks by Guifre Vidal and Xiao-Gang Wen : ^)

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

 

[inflector]

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

Check out his paper with Ashvin Vishwanath of the same title from January:

http://arxiv.org/abs/1401.3736

'Gauging' time reversal symmetry in tensor network states
Xie Chen, Ashvin Vishwanath
Abstract:

It is well know that unitary symmetries can be `gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry. Here we discuss a route to gauging time reversal symmetry that applies to gapped quantum ground states. We show how time reversal can be applied locally and also describe time reversal symmetry twists which act as gauge fluxes through nontrivial loops in the system. The procedure is based on the tensor network representation of quantum states which provides a notion of locality for the wave function coefficient. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain symmetry protected topological phases in D=1,2 are readily extracted using these ideas and also discuss how they help capture a subtle distinction between time reversal symmetric Z2 gauge theories.​

 

[marcus]

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

She was a postdoc for 2 years at Berkeley in Ashvin Vishwanath's group:
https://sites.google.com/site/ashvinvish/Home/people
and in July 2014 moved to Caltech to take a faculty position. Bright young person in what seems like a good field of research to be in. A kind of combination of Quantum Information theory and Condensed Matter?
Here's a Caltech blurb about her joining the faculty
http://www.caltech.edu/news/quantum-information-meets-condensed-matter-inside-mind-xie-chen-43439
She got her PhD at MIT, I vaguely remember her co-authoring with Xiao-Gang Wen, maybe he was her advisor.

 

[atyy]

At the end of his talk, Physics Monkey argues that one can actually get the nonlinear Einstein equations (he just mentions it without much detail, the talk is mainly about the linearized equation). I think so far the published papers only say how to get the linearized Einstein equations, so that should be an interesting paper to wait for.

 

[marcus]

At the end of his talk, Physics Monkey argues that one can actually get the nonlinear Einstein equations (he just mentions it without much detail, the talk is mainly about the linearized equation). I think so far the published papers only say how to get the linearized Einstein equations, so that should be an interesting paper to wait for.

You already gave the link to Physics Monkey's talk, but we've turned a page so I'll bring it forward:
http://simons.berkeley.edu/talks/brian-swingle-2014-04-22
Einstein's Equations Starting from Qubits
Brian Swingle, Harvard University

I was not aware of published papers deriving linearized GR, so one of us should probably post links here as a convenience for anyone who wants to check out what versions of Einstein's equations are being derived from what. It's all pretty interesting! You may recall the LQG paper by Chirco et al which derives the full non-linear Einstein GR equation from quantum gravity degrees of freedom---by showing that it can indeed be viewed as a thermodynamic equation of state (as Jacobson already proved in 1995), but of specific microscopic QG (rather than unknown "hidden" variables, as Jacobson originally suggested).
http://arxiv.org/abs/1401.5262
Spacetime thermodynamics without hidden degrees of freedom
Goffredo Chirco, Hal M. Haggard, Aldo Riello, Carlo Rovelli
(Submitted on 21 Jan 2014)
A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.
12 pages, 1 figure

 

[atyy]

http://arxiv.org/abs/1412.0687
Entanglement entropy in three dimensional gravity
Henry Maxfield
(Submitted on 1 Dec 2014)
The Ryu-Takayanagi and covariant Hubeny-Rangamani-Takayanagi proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotients of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.

 

[atyy]

http://arxiv.org/abs/1412.1879
Tomography from Entanglement
Jennifer Lin, Matilde Marcolli, Hirosi Ooguri, Bogdan Stoica
(Submitted on 5 Dec 2014)
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory, follow from positivity conditions on the bulk matter energy density. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

http://arxiv.org/abs/1412.1895
Entanglement entropy of electromagnetic edge modes
William Donnelly, Aron C. Wall
(Submitted on 5 Dec 2014)
The vacuum entanglement entropy of Maxwell theory, when evaluated by standard methods, contains an unexpected term with no known statistical interpretation. We resolve this two-decades old puzzle by showing that this term is the entanglement entropy of edge modes: classical solutions determined by the electric field normal to the entangling surface. We explain how the heat kernel regularization applied to this term leads to the negative divergent expression found by Kabat. This calculation also resolves a recent puzzle concerning the logarithmic divergences of gauge fields in 3+1 dimensions.

 

[atyy]

http://arxiv.org/abs/1412.4220
Analog Systems for Gravity Duals
S. Hossenfelder
(Submitted on 13 Dec 2014)
We show that analog gravity systems exist for charged, planar black holes in asymptotic Anti-de Sitter space. These black holes have been employed to describe, via the gauge-gravity duality, strongly coupled condensed matter systems on the boundary of AdS-space. The analog gravity system is a different condensed matter system that, in a suitable limit, describes the same bulk physics as the theory on the AdS boundary. This combination of the gauge-gravity duality and analog gravity therefore suggests a duality between different condensed matter systems.

 

[atyy]

http://arxiv.org/abs/1412.8483
ER=EPR, GHZ, and the Consistency of Quantum Measurements
Leonard Susskind
(Submitted on 29 Dec 2014)
This paper illustrates various aspects of the ER=EPR conjecture.It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges.
The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-Zeilinger pattern.
The last part of the paper is about entanglement as a resource for quantum communication. ER=EPR provides a way to visualize protocols like quantum teleportation. In some sense teleportation takes place through the wormhole, but as usual, classical communication is necessary to complete the protocol.

 

[marcus]

http://arxiv.org/abs/1501.00003
Holographic entanglement entropy and the internal space
Andreas Karch, Christoph F. Uhlemann
(Submitted on 30 Dec 2014)
We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS₅×S⁵, their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS₅×S⁵ geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.
11 pages, 6 figures

 

[atyy]

http://arxiv.org/abs/1501.00007
The AdS/CFT Correspondence
Veronika E. Hubeny
(Submitted on 30 Dec 2014)
We give a brief review of the AdS/CFT correspondence, which posits the equivalence between a certain gravitational theory and a lower-dimensional non-gravitational one. This remarkable duality, formulated in 1997, has sparked a vigorous research program which has gained in breadth over the years, with applications to many aspects of theoretical (and even experimental) physics, not least to general relativity and quantum gravity. To put the AdS/CFT correspondence in historical context, we start by reviewing the relevant aspects of string theory (of which no prior knowledge is assumed). We then develop the statement of the correspondence, and explain how the two sides of the duality map into each other. Finally, we discuss the implications and applications of the correspondence, and indicate some of the current trends in this subject. The presentation attempts to convey the main concepts in a simple and self-contained manner, relegating supplementary remarks to footnotes.

 

[marcus]

http://arxiv.org/abs/1501.01408
Quantum Gravity as an Information Network: Self-Organization of a 4D Universe
Carlo A. Trugenberger
(Submitted on 7 Jan 2015)
I propose a quantum gravity model in which the fundamental degrees of freedom are pure information bits. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links between them. As a result of the frustration arising between these two terms, the ground state self-organizes as a new type of low-clustering, lattice-like graph with finite Hausdorff dimension. The model has three quantum phases: a mean field phase in which the spectral and Hausdorff dimensions coincide and are larger then 4. A fluctuations-dominated phase in which the Hausdorff dimension can only be 4 and the spectral dimension is lower than the Hausdorff dimension and a disordered phase in which there is no space-time interpretation. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. An ultraviolet fixed point at the lower critical dimension of the Ising model is conjectured to imply the absence of space-time at very small scales. At finite temperatures the universe emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe unfolds by lowering its connectivity, a mechanism I have called topological expansion. Topological expansion is associated with one emerging dimension describing the unfolding process. Quantum fluctuations about this semiclassical universes are elementary black holes and wormholes. The model admits, however, also macroscopic black hole configurations corresponding to graphs containing holes with no space time inside and around which there are Schwarzschild-like horizons with a lower spectral dimension and an entropy proportional to their area.
12 pages, several tables.
[Atyy let me know if this paper does not fit in with the theme and direction of your bibliography. I will of course be happy to remove it.]