Condensed matter physics, area laws & LQG?

[atyy]

I don't understand this paper. For example, why assume the perfect canonical ensemble for so few particles?

Did you mean that they should have used the microcanonical ensemble, and the canonical ensemble only makes sense or agrees with the microcanonical in the thermodynamic limit?

 

[Physics Monkey]

That would be one possibility. More generally, why, in an isolated system with no interactions, should I use any thermodynamic ensemble at all? What if the system is in a pure state? Will arbitrarily small interactions change things?

Furthermore, if thermalization is imagined to take place due to interactions with the wall or some bath, the bath-system entanglement might be important. One certainly won't get exactly the state being considered if one traces over the bath.

I also worry about the role of (presumably large) fluctuations in this setup.

I suppose the point is that we do understand very well how phase transitions effectively arise with finite systems and I'm just not sure what I'm supposed to be learning from this calculation. I don't want to be too harsh, I just don't get it.

 

[marcus]

This could be of interest in the context of this thread :
http://arxiv.org/abs/1310.8372
Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
Glen Evenbly, Guifre Vidal
(Submitted on 31 Oct 2013)
We investigate the scaling of entanglement entropy in both the multi-scale entanglement renormalization ansatz (MERA) and in its generalization, the branching MERA. We provide analytical upper bounds for this scaling, which take the general form of a boundary law with various types of multiplicative corrections, including power-law corrections all the way to a bulk law. For several cases of interest, we also provide numerical results that indicate that these upper bounds are saturated to leading order. In particular we establish that, by a suitable choice of holographic tree, the branching MERA can reproduce the logarithmic multiplicative correction of the boundary law observed in Fermi liquids and spin-Bose metals in D≥2 dimensions.
17 pages, 14 figures

 

[atyy]

https://www.physicsforums.com/showpost.php?p=4555721&postcount=9

My pick for the 4th quarter:

http://arxiv.org/abs/1310.7786

Group field theory as the 2nd quantization of Loop Quantum Gravity

Daniele Oriti
(Submitted on 29 Oct 2013)
We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.

"The simple but key point of the construction is to realize in which sense LQG states (which we call here generically 'spin network states', even if this name would only strictly apply to LQG states in the spin representation) can be understood as "many-particle" states analogously to those found in particle physics and condensed matter theory."

 

[atyy]

http://arxiv.org/abs/1311.1137
Behind the Horizon in AdS/CFT
Erik Verlinde, Herman Verlinde
(Submitted on 5 Nov 2013)
We extend the recent proposal of Papadodimas and Raju of a CFT construction of operators inside the black hole interior to arbitrary non-maximally mixed states. Our construction builds on the general prescription given in earlier work, based on ideas from quantum error correction. We indicate how the CFT state dependence of the interior modes can be removed by introducing an external system, such as an observer, that is entangled with the CFT.

http://arxiv.org/abs/1311.1784
Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
Tian Lan, Xiao-Gang Wen
(Submitted on 7 Nov 2013)
String-net models allow us to systematically construct and classify 2+1D topologically ordered states which can have gapped boundaries. So we can use the simple ideal string-net wavefunctions to study all the universal properties of such topological orders. In this paper, we describe a finite computational method -- Q-algebra module approach, that allows us to compute the non-Abelian statistics of the topological excitations [described by a modular tensor category (MTC)] from the string-net wavefunction [described by a unitary fusion category (UFC)]: MTC=Z(UFC), where Z is the functor that takes the Drinfeld center. We discuss several examples, including the twisted quantum double Dα(G) phase. Our result can also be viewed from an angle of holographic bulk-boundary relation. The 2+1D topological orders are classified by MTC plus the chiral central charge of the edge states, while the 1+1D anomalous topological orders (that appear on the edge of 2+1D gapped states) are classified by UFC. If we know an edge (described by a UFC) of a gapped 2+1D state, then our method allows us to compute the bulk topological order [described by a MTC=Z(UFC) with zero chiral central charge].

http://arxiv.org/abs/1311.1798
Topological lattice field theories from intertwiner dynamics
Bianca Dittrich, Wojciech Kaminski
(Submitted on 7 Nov 2013)
We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.

 

[atyy]

http://arxiv.org/abs/1311.1643
Volume Law for the Entanglement Entropy in Non-local QFTs
Noburo Shiba, Tadashi Takayanagi
(Submitted on 7 Nov 2013 (v1), last revised 14 Nov 2013 (this version, v2))
In this paper, we present a simple class of non-local field theories whose ground state entanglement entropy follows a volume law as long as the size of subsystem is smaller than a certain scale. We will confirm this volume law both from numerical calculations and from analytical estimation. This behavior fits nicely with holographic results for spacetimes whose curvatures are much smaller than AdS spaces such as those in the flat spacetime.

 

[atyy]

http://arxiv.org/abs/1311.3327
Area law violation for the mutual information in a nonequilibrium steady state
Viktor Eisler, Zoltan Zimboras
(Submitted on 13 Nov 2013)
We study the nonequilibrium steady state of an infinite chain of free fermions, resulting from an initial state where the two sides of the system are prepared at different temperatures. The mutual information is calculated between two adjacent segments of the chain and is found to scale logarithmically in the subsystem size. This provides the first example of the violation of the area law in a quantum many-body system outside a zero temperature regime. The prefactor of the logarithm is obtained analytically and, furthermore, the same prefactor is shown to govern the logarithmic increase of mutual information in time, before the system relaxes locally to the steady state.

 

[atyy]

http://arxiv.org/abs/1311.6095
Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
Ali Mollabashi, Masahiro Nozaki, Shinsei Ryu, Tadashi Takayanagi
(Submitted on 24 Nov 2013)
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal of arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.

 

[marcus]

This Loop paper by Dittrich et al. cites research by B. Swingle and also by G. Vidal. Swingle's paper, for instance, is cited both on page 2 in the introduction and on page 28 of the conclusions [31].
http://arxiv.org/abs/1311.7565
Time evolution as refining, coarse graining and entangling
Bianca Dittrich, Sebastian Steinhaus
(Submitted on 29 Nov 2013)
We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.
33 pages, 9 figures

 

[marcus]

Does anyone want to clarify what is going on in this paper?
We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.

If that is confirmed applicable in general it would be important: consistent continuum limit! Why should the construction parallel time-evolution?

I've tried reading the paper, but have more than usual difficulty understanding it. There are a bunch of diagrams of Pachner moves that can implement either refinement (in one direction) or coarsegraining (in the other direction). Some other diagrams illustrate moves which produce entanglement. Simpler Pachner move diagrams I don't have trouble reading. It might help if these were redrawn with dotted lines and bold lines giving more hints as to how to read them.

Also I must say I don't grasp the connection with the papers by Swingle and by Vidal, which connection Dittrich considers important enough to emphasize both in the introduction and at the end of the paper in the conclusions.

 

[atyy]

Dittrich and Steinhaus's main point is very non-intiutive point (to me). "In this note we point out that time evolution maps, that appear in simplicial discretizations [13, 14], can also be interpreted as refining and coarse graining maps. As we will argue here this applies in particular to gravitational dynamics, e.g. spin foams [15, 16, 17, 18]."

For them it's "obvious"! "The idea that time evolution can be interpreted as coarse graining, refining or entangling occurs in many approaches, indeed many points we make in this note may be obvious. Tensor network coarse graining algorithm can be easily seen as time evolution in radial direction (in an Euclidean space time), which itself leads to holographic renormalization [29]."

Looks like it'll be a very interesting read!

 

[marcus]

Today Dittrich and Steinhaus, joined by a third author also based at Perimeter, posted a second paper on the same general topic as the one mentioned a couple of posts back.
http://arxiv.org/abs/arXiv:1312.0905
Quantum group spin nets: refinement limit and relation to spin foams
Bianca Dittrich, Mercedes Martin-Benito, Sebastian Steinhaus
(Submitted on 3 Dec 2013)
So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups SU(2)_k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.
30+5 pages, many figures

==excerpt from conclusions==
In this work we have taken several important steps towards a full understanding of the continuum limit of spin foam models. We in particular introduced and defined models based on the structure group SU(2)k that can encode the dynamics of the full gravitational models, but are still feasible to investigate numerically. Note that apart from certain technical subtleties (e.g. the definition of the duals) for the quantum group coarse graining, that we resolved, this nevertheless requires very efficient numerical algorithms19. For this the symmetry protected tensor network algorithm developed here and in [21] is absolutely crucial.
We considered mainly spin nets, as dimensional reductions of spin foams, in this work…
==endquote==
Among other people, they thank G. Vidal in the acknowledgments. Citations include a fair number of unpublished and w.i.p. items.

 

[atyy]

Is this paper right?

http://arxiv.org/abs/1108.0320
Unruh effect without trans-horizon entanglement
Carlo Rovelli, Matteo Smerlak
Since in this setup the state of the field in the Rindler wedge is pure, we argue furthermore that the relevant entropy in the Unruh effect cannot be the von Neumann entanglement entropy. We suggest, in alternative, that it is the Shannon entropy associated with Heisenberg uncertainty.

 

[marcus]

Is this paper right?

http://arxiv.org/abs/1108.0320
Unruh effect without trans-horizon entanglement
Carlo Rovelli, Matteo Smerlak
Since in this setup the state of the field in the Rindler wedge is pure, we argue furthermore that the relevant entropy in the Unruh effect cannot be the von Neumann entanglement entropy. We suggest, in alternative, that it is the Shannon entropy associated with Heisenberg uncertainty.

I think it probably is right, if you read carefully what it says. It is talking about the Unruh effect as described in Unruh's original paper, on an accelerating detector. As they say in the paper if you mean something else by "Unruh effect" then it can be correct to attribute it to entanglement entropy as is often done. But if you focus on the thermality of the detector clicks then they argue there is more to the story.Is there a connection with some of the other discussion, and papers mentioned in this thread?

For clarity, I'll quote the full abstract, since in the fragment of it you quoted it is not clear what "this setup" is and what Unruh effect they are talking about.
==quote==
We estimate the transition rates of a uniformly accelerated Unruh-DeWitt detector coupled to a quantum field with reflecting conditions on a boundary plane (a “mirror”). We find that these are essentially indistinguishable from the usual Unruh rates, viz. that the Unruh effect persists in the presence of the mirror. This shows that the Unruh effect (thermality of detector rates) is not merely a consequence of the entanglement between left and right Rindler quanta in the Minkowski vacuum. Since in this setup the state of the field in the Rindler wedge is pure, we argue furthermore that the relevant entropy in the Unruh effect cannot be the von Neumann entanglement entropy. We suggest, in alternative, that it is the Shannon entropy associated with Heisenberg uncertainty.
==endquote==

Something to notice about 1108.0320 is that it was submitted to Physical Review D on 4 August 2011 and the final version [v3] was published in PRD on 25 June 2012, almost 11 months later.
http://prd.aps.org/abstract/PRD/v85/i12/e124055
There was no mathematical or logical change that I can see. But in April 2012 a paragraph (highlighted) was added in the introduction which simply repeats and emphasizes a crucial distinction which had already been remarked briefly, in passing, in the first paragraph.
It's possible that a reader of the first version might have MISSED that crucial point.
==excerpt page 1==

An accelerated particle detector clicks even in the vacuum. This is not surprising per se: the detector receives energy from whichever device is accelerating it, and there is no reason why this energy should not be exchanged with the field. What is surprising, however, is the thermal character of these transitions in the case of uniform acceleration, discovered by Unruh [1]: thermal states are states of maximal entropy—whence the entropy of “acceleration radiation”?…
...In this light, the entropy of the Unruh radiation appears to be related to the von Neumann entropy of the improper mixture of right Rindler quanta [6, 7].

If by “Unruh effect” one means the thermal character of the vacuum field fluctuations observable within a Rindler wedge, this is clearly correct. But if we restrict the attention just to the detector’s transition rates, and by “Unruh effect” one means—as in Unruh’s original work and as we do here—the thermal character of the detector’s transition rates, then, we argue here, the story is subtler and there is more to learn.

A difficulty with the entanglement interpretation of the Unruh effect (in the sense specified) has been pointed out repeatedly, e.g. in [9–11]: it violates causality. The Rindler horizon of an accelerated observer depends on its entire worldline, with proper time ranging from minus to plus infinity. But a physical effect cannot depend on the future history of the observer. This motivated Schlicht to study the Unruh effect in causal terms [10]; he concluded…
==endquote==

 

[atyy]

Thanks marcus. The Rovelli-Smerlak http://arxiv.org/abs/1108.0320 does make sense given that they are looking only for the detector transition rates. It's related to this thread, because the idea that the Rindler wedge is thermal by tracing out the environment on a pure state in Minkowski space features in many heuristics about spacetime being made from entanglement, firewalls etc. For example, Czech et al's http://arxiv.org/abs/1206.1323 uses the idea that if a state on the Rindler wedge is not entangled with stuff outside the wedge, then the energy density diverges at the boundary of the wedge - like a firewall. So by analogy of the Rindler wedge to a black hole, if the outside is not entangled with the inside, there would be a firewall. The Rindler wedge is also one of the examples in the Connes-Rovelli thermal time paper http://arxiv.org/abs/gr-qc/9406019 , as well as the Bianchi-Myers http://arxiv.org/abs/1212.5183 .

 

[marcus]

It helps to see it explained that way. There's another paper that might interest you if you haven't already seen it.
I'm not sure whether or not it fits in thematically or not with this thread. It's Freidel's most recent. Here's what he says in the introduction:
==quote http://arxiv.org/abs/1312.1538 ==
Unlike any other interactions, gravity is fundamentally holographic. This fundamental property of Einstein gravity manifests itself more clearly when one tries to define a notion of energy for a gravitational system. It is well known that no local covariant notion of energy can be given in general relativity. The physical reason can be tracked to the equivalence principle. Illustrated in a heuristic manner, a free falling point-like particle does not feel any gravitational field, so no gravitational energy density can be identified at spacetime points. A more radical way to witness the holographic nature of gravity, comes from the fact that the Hamiltonian of general relativity coupled to any matter fields, exactly vanishes for any physical configuration of the fields. If one asks what is the total energy of a closed gravitational system with no boundary, the answer is that it is zero for any physical configurations. This is a mathematical consequence of diffeomorphism invariance. It naively implies that the gravitational energy density vanish.
A proper way to accommodate this, is to recognize that a notion of energy can only be given once we introduce a bounded region of space together with a time evolution for the boundary of this region. The time evolution of this boundary span a timelike world tube equipped with a time foliation. We will call such boundaries equipped with a timelike foliation, gravitational screens. They will be the subject of our study which focuses on what happen to a gravitational system in a finite bounded region. In the presence of gravity, the total energy of the region inside the screen comes purely from a boundary screen contribution and the bulk contribution vanishes. In that sense, energy cannot be localized but it can be quasi-localized, i-e expressed as a local surface integral on the screen…
==endquote==

 

[marcus]

On page 12 he gives a surface integral definition of the energy of the gravitational field. Equation (40).
==quote Freidel==
Let us emphasize here that this energy formula, presents two key features. First, it is quasi-local: it is non vanishing only on the boundary of the region of observation. This is a consequence of diffeomorphism invariance which implies that the bulk Hamiltonian vanish. In this sense gravity is naturally holographic.
Second, the energy depends on the choice of observer, that is not only the choice of screens, but also the choice of foliation of the screens. This second feature is not that unusual, for instance…
==endquote==
The title of the paper is: "Gravitational Energy, Local Holography and Non-Equilibrium Thermodynamics".
I am beginning to feel more confident that it fits thematically into this thread, but you must judge that.
I like it that the arguments are simple, from first principles, and the concepts are basic. (there has always been this problem with the energy of the gravitational field, the definition hasn't been satisfactory, maybe this paper is foundational enough to help arrive at a satisfactory idea of it. Also the entropy of the gravitational field has not been satisfactorily defined so far, I think, and hopefully Freidel may be making some progress there as well…)

He also goes into some detail about the antecedents and inspirations from prior research by other people (Thorne, Damour…). There has certainly been a lot of prior research. So you get a sense of historical direction by reading the paper, perhaps a new perspective on the significance of past work.

 

[marcus]

Billed as a "Joint Condensed Matter/Quantum Gravity Seminar" -- sound familiar?

We've been posting recent Dittrich papers and there's a video presentation she gave three days ago on a related topic. It says it's based on the same papers we've noted in this thread:
==quote==
http://pirsa.org/13120048/
From spin foams to anyons and back again - Joint Condensed Matter/Quantum Gravity Seminar
Speaker(s): Bianca Dittrich
Abstract: Spin foams provide models for quantum gravity and hence quantum space time. One of the key outstanding questions is to show that they reproduce smooth space time manifolds in a continuum limit.I will start with a very short introduction to spin foams and the structure of quantum space time they encode. I will explain how the investigation of the continuum limit via coarse graining and renormalization techniques led as to consider anyonic spin chains and a classification of ground states in systems with quantum group symmetries.I will then present new results on the continuum limit of spin net models, that allow us to draw first conclusions about the large scale dynamics of spin foams.
Based on: B.D., W. Kaminski, Topological lattice field theories from intertwiner dynamics, arXiv:1311.1798, B.D., S. Steinhaus, Time evolution as refining, coarse graining and entangling, to appear, B.D. M. Martin-Benito, S. Steinhaus, The refinement limit of quantum group spin net models, to appear
Date: 05/12/2013 - 2:30 pm
==endquote==
The three papers are logged in posts #145, 149, 152 of this thread. The "to appear" papers have in fact appeared.

 

[marcus]

There's a curious resonance between the latest paper by Padmanabhan and the Freidel paper discussed back a ways in posts#156 and 157.
http://arxiv.org/abs/1312.1538
Gravitational Energy, Local Holography and Non-Equilibrium Thermodynamics
Laurent Freidel

...Here's what he says in the introduction:
==quote http://arxiv.org/abs/1312.1538 ==
Unlike any other interactions, gravity is fundamentally holographic. This fundamental property of Einstein gravity manifests itself more clearly when one tries to define a notion of energy for a gravitational system. It is well known that no local covariant notion of energy can be given in general relativity. The physical reason can be tracked to the equivalence principle. Illustrated in a heuristic manner, a free falling point-like particle does not feel any gravitational field, so no gravitational energy density can be identified at spacetime points. A more radical way to witness the holographic nature of gravity, comes from the fact that the Hamiltonian of general relativity coupled to any matter fields, exactly vanishes for any physical configuration of the fields. If one asks what is the total energy of a closed gravitational system with no boundary, the answer is that it is zero for any physical configurations. This is a mathematical consequence of diffeomorphism invariance. It naively implies that the gravitational energy density vanish.
A proper way to accommodate this, is to recognize that a notion of energy can only be given once we introduce a bounded region of space together with a time evolution for the boundary of this region. The time evolution of this boundary span a timelike world tube equipped with a time foliation. We will call such boundaries equipped with a timelike foliation, gravitational screens. They will be the subject of our study which focuses on what happen to a gravitational system in a finite bounded region. In the presence of gravity, the total energy of the region inside the screen comes purely from a boundary screen contribution and the bulk contribution vanishes. In that sense, energy cannot be localized but it can be quasi-localized, i-e expressed as a local surface integral on the screen…
==endquote==

==quote Freidel page 12, on equation (40) energy of gravitational field==
Let us emphasize here that this energy formula, presents two key features. First, it is quasi-local: it is non vanishing only on the boundary of the region of observation. This is a consequence of diffeomorphism invariance which implies that the bulk Hamiltonian vanish. In this sense gravity is naturally holographic.
Second, the energy depends on the choice of observer, that is not only the choice of screens, but also the choice of foliation of the screens. This second feature is not that unusual, for instance…
==endquote==
...

Here, for comparison, is Padmanabhan's latest
http://arxiv.org/abs/1312.3253
General Relativity from a Thermodynamic Perspective
T. Padmanabhan
(Submitted on 11 Dec 2013)
Several recent results suggest that gravity is an emergent phenomenon with its field equations having the same status as, say, the equations of fluid dynamics. I describe several additional results, supporting this paradigm and connecting the gravitational dynamics in a bulk region of space with a thermodynamic description in the boundary of that region: (1) The Noether charge contained in a bulk region, associated with a specific time evolution vector field, has a direct thermodynamic interpretation as the gravitational heat content of the boundary surface. (2) This result, in turn, shows that all static spacetimes maintain holographic equipartition; in these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk. (3) In a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. It is this departure from the holographic equipartition which drives the time evolution of the spacetime. (4) When the equations of motion hold, the (naturally defined) total energy of the gravity plus matter within a bulk region, will be equal to the boundary heat content. (5) After motivating the need for an alternate description of gravity (if we have to solve the cosmological constant problem), I describe a thermodynamic variational principle based on null surfaces to achieve this goal. The concept of gravitational heat density of the null surfaces arises naturally from the Noether charge associated with the null congruence. The null surface variational principle, in fact, extremises the total heat content of the matter plus gravity system. Several variations on this theme and implications are described. [Abridged]
53 pages

I notice in both cases they use a holo "boundary-bulk" setup to define the gravitational energy, and also to get a handle on the directionality of time-evolution.

 

[atyy]

Heretics! :p

http://arxiv.org/abs/1312.3346
No Holography for Eternal AdS Black Holes
Steven G. Avery, Borun D. Chowdhury
(Submitted on 11 Dec 2013)
It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforementioned caps will be fuzzballs.

 

[atyy]

http://arxiv.org/abs/1312.3699
Extremal Surface Barriers
Netta Engelhardt, Aron C. Wall
(Submitted on 13 Dec 2013)
We present a generic condition for Lorentzian manifolds to have a barrier that limits the reach of boundary-anchored extremal surfaces of arbitrary dimension. We show that any surface with nonpositive extrinsic curvature is a barrier, in the sense that extremal surfaces cannot be continuously deformed past it. Furthermore, the outermost barrier surface has nonnegative extrinsic curvature. Under certain conditions, we show that the existence of trapped surfaces implies a barrier, and conversely. In the context of AdS/CFT, these barriers imply that it is impossible to reconstruct the entire bulk using extremal surfaces. We comment on the implications for the firewall controversy.

 

[atyy]

http://arxiv.org/abs/1312.5646
Ising Model from Intertwiners
Bianca Dittrich, Jeff Hnybida
(Submitted on 19 Dec 2013)
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of intertwiner contractions leads to the partition function of the 2d Ising model. This implies that the intertwiner model possesses a second order phase transition, thus leading to a continuum limit with propagating degrees of freedom.

 

[atyy]

Lubos Motl has some interesting comments about the paper by Avery and Chowdhury in post#160: http://motls.blogspot.com/2013/12/avery-chowdhury-criticism-of-er-epr-is.html.

 

[marcus]

I recall you branded them "Heretics!" in any case it's interesting that there's some argument about ER=EPR. I wonder how the rest of the community will react to the *ry-*ry paper.

 

[atyy]

http://arxiv.org/abs/1312.6717
General properties of holographic entanglement entropy
Matthew Headrick
(Submitted on 23 Dec 2013)
The Ryu-Takayanagi formula implies many general properties of entanglement entropies in holographic theories. We review the known properties, such as continuity, strong subadditivity, and monogamy of mutual information, and fill in gaps in some of the previously-published proofs. We also add a few new properties, including: properties of the map from boundary regions to bulk regions implied by the RT formula, such as monotonicity; conditions under which subadditivity-type inequalities are saturated; and an inequality concerning reflection-symmetric states. We attempt to draw lessons from these properties about the structure of the reduced density matrix in holographic theories.

http://arxiv.org/abs/1312.6887
Holographic probes of collapsing black holes
Veronika E. Hubeny, Henry Maxfield
(Submitted on 24 Dec 2013)
We continue the programme of exploring the means of holographically decoding the geometry of spacetime inside a black hole using the gauge/gravity correspondence. To this end, we study the behaviour of certain extremal surfaces (focusing on those relevant for equal-time correlators and entanglement entropy in the dual CFT) in a dynamically evolving asymptotically AdS spacetime, specifically examining how deep such probes reach. To highlight the novel effects of putting the system far out of equilibrium and at finite volume, we consider spherically symmetric Vaidya-AdS, describing black hole formation by gravitational collapse of a null shell, which provides a convenient toy model of a quantum quench in the field theory. Extremal surfaces anchored on the boundary exhibit rather rich behaviour, whose features depend on dimension of both the spacetime and the surface, as well as on the anchoring region. The main common feature is that they reach inside the horizon even in the post-collapse part of the geometry. In 3-dimensional spacetime, we find that for sub-AdS-sized black holes, the entire spacetime is accessible by the restricted class of geodesics whereas in larger black holes a small region near the imploding shell cannot be reached by any boundary-anchored geodesic. In higher dimensions, the deepest reach is attained by geodesics which (despite being asymmetric) connect equal time and antipodal boundary points soon after the collapse; these can attain spacetime regions of arbitrarily high curvature and simultaneously have smallest length. Higher-dimensional surfaces can penetrate the horizon while anchored on the boundary at arbitrarily late times, but are bounded away from the singularity. We also study the details of length or area growth during thermalization. While the area of extremal surfaces increases monotonically, geodesic length is neither monotonic nor continuous.

 

[atyy]

http://arxiv.org/abs/1312.6861
Kenneth Geddes Wilson
Andreas S. Kronfeld
(Submitted on 24 Dec 2013)
A look back at Kenneth Wilson's contributions to theoretical physics, with some reminiscences of the professor I encountered at Cornell during the 1980s.

Kenneth Wilson was one of the fathers of renormalization and lattice gauge theory, both of which are concerns of all three fields (condensed matter, string theory, LQG) that this thread is interested in.

 

[atyy]

http://arxiv.org/abs/1312.6914
Geometric RG Flow
Steven Jackson, Razieh Pourhasan, Herman Verlinde
(Submitted on 25 Dec 2013)
We define geometric RG flow equations that specify the scale dependence of the renormalized effective action Gamma[g] and the geometric entanglement entropy S[x] of a QFT, considered as functionals of the background metric g and the shape x of the entanglement surface. We show that for QFTs with AdS duals, the respective flow equations are described by Ricci flow and mean curvature flow. For holographic theories, the diffusion rate of the RG flow is much larger, by a factor $R_{AdS}^2/\ell_s^2$, than the RG resolution length scale. To derive our results. we employ the Hamilton-Jacobi equations that dictate the dependence of the total bulk action and the minimal surface area on the geometric QFT boundary data.

http://arxiv.org/abs/1312.7119
Superconducting and Anti-Ferromagnetic Phases of Spacetime
Deepak Vaid
(Submitted on 26 Dec 2013)
A correspondence between the SO(5) theory of High-TC superconductivity and antiferromagnetism, put forward by Zhang and collaborators, and a theory of gravity arising from symmetry breaking of a SO(5) gauge field is presented. A physical correspondence between the order parameters of the unified SC/AF theory and the generators of the gravitational gauge connection is conjectured. A preliminary identification of regions of geometry, in solutions of Einstein's equations describing charged-rotating black holes embedded in deSitter spacetime, with SC and AF phases is carried out.

 

[atyy]

Posted by John86 in marcus's bibliography https://www.physicsforums.com/showpost.php?p=4616837&postcount=2103:

http://arxiv.org/abs/1312.7856
Gravitation from Entanglement in Holographic CFTs
Thomas Faulkner, Monica Guica, Thomas Hartman, Robert C. Myers, Mark Van Raamsdonk
(Submitted on 30 Dec 2013)
Entanglement entropy obeys a 'first law', an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S=A/(4GN), we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.

 

[atyy]

Pointed out by marcus in his bibliography https://www.physicsforums.com/showpost.php?p=4619210&postcount=2104

http://arxiv.org/abs/1401.0288
Disentangling the Black Hole Vacuum
S. Hossenfelder
(Submitted on 1 Jan 2014)
We study the question whether disentanglement of Hawking radiation can be achieved with any local operation. We assume that the operation we look for is unitary and can be described by a Bogoliubov transformation. This allows to formulate requirements on the operation of disentanglement. We then show that these requirements can be fulfilled by a timelike boundary condition in the near-horizon area and that the local observer does not notice the presence of the boundary and does not encounter a firewall.

 

[atyy]

http://arxiv.org/abs/1401.3341
Holographic Space-time and Black Holes: Mirages As Alternate Reality
Tom Banks, Willy Fischler, Sandipan Kundu, Juan F. Pedraza
(Submitted on 14 Jan 2014)
We revisit our investigation of the claim of [1] that old black holes contain a firewall, i.e. an in-falling observer encounters highly excited states at a time much shorter than the light crossing time of the Schwarzschild radius. We used the formalism of Holographic Space-time (HST) where there is no dramatic change in particle physics inside the horizon until a time of order the Schwarzschild radius. We correct our description of the interior of the black hole . HST provides a complete description of the quantum mechanics along any time-like trajectory, even those which fall through the black hole horizon. The latter are described as alternative factorizations of the description of an external observer, turning the mirage of the interior provided by that observer's membrane paradigm on the stretched horizon, into reality.

Spotted by John86 in marcus's bibliography http://arxiv.org/abs/1401.3416:

http://arxiv.org/abs/1401.3416
Wormholes and Entanglement
John C. Baez, Jamie Vicary
(Submitted on 15 Jan 2014)
Maldacena and Susskind have proposed a correspondence between wormholes and entanglement, dubbed ER=EPR. We study this in the context of 3d topological quantum field theory, where we show that the formation of a wormhole is the same process as creating a particle-antiparticle pair. A key feature of the ER=EPR proposal is that certain apparently entangled degrees of freedom turn out to be the same. We name this phenomenon "fake entanglement", and show how it arises in our topological quantum field theory model.

 

[atyy]

http://arxiv.org/abs/1305.0011
Emergent Lorentz invariance from Strong Dynamics: Holographic examples
Grigory Bednik, Oriol Pujolas, Sergey Sibiryakov
(Submitted on 30 Apr 2013 (v1), last revised 4 Sep 2013 (this version, v2))
We explore the phenomenon of emergent Lorentz invariance in strongly coupled theories. The strong dynamics is handled using the gauge/gravity correspondence. We analyze how the renormalization group flow towards Lorentz invariance is reflected in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are found to be power-law suppressed by the ratio of the infrared and ultraviolet scales. We show that in a certain subclass of models the velocities of the light bound states stay close to the emergent `speed of light' even at high energies. We comment on the implications of our results for particle physics and condensed matter.

http://arxiv.org/abs/1401.5003
Renormalization: an advanced overview
Razvan Gurau, Vincent Rivasseau, Alessandro Sfondrini
(Submitted on 20 Jan 2014)
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.

 

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Pointed out by marcus in his bibliography https://www.physicsforums.com/showthread.php?t=7245#post4637315.

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.

 

[marcus]

Entanglement entropy is a key concept in the CHRR paper and the authors base their approach on papers by E. Bianchi and R. Myers (their references [4] and [5]). It is interesting to note how much the CHRR paper, which I think is a major advance, fits in with the themes you have developed in this thread. Readers could look back, for example, to your post #168. But that's just one of many--IIRC there is plenty more on the general topic "gravity from entanglement"

 

[atyy]

http://arxiv.org/abs/1402.4829
From state distinguishability to effective bulk locality
Nima Lashkari, Joan Simon
(Submitted on 19 Feb 2014)
We provide quantitative evidence that the emergence of an effective notion of spacetime locality in black hole physics is due to restricting to the subset of observables that are unable to resolve black hole microstates from the maxi- mally entangled state. We identify the subset of observables in the full quantum theory that can distinguish microstates, and argue that any measurement of such observables involves either long times or large energies, both signaling the breaking down of effective field theory where locality is manifest. We discuss some of the implications of our results for black hole complementarity and the existence of black hole interiors.

 

[atyy]

http://arxiv.org/abs/1403.0951
Spacetime Entanglement with f(R) Gravity
Razieh Pourhasan
(Submitted on 4 Mar 2014)
We study the entanglement entropy of a general region in a theory of induced gravity using holographic calculations. In particular we use holographic entanglement entropy prescription of Ryu-Takayanagi in the context of the Randall-Sundrum 2 model while considering general f(R) gravity in the bulk. Showing the leading term is given by the usual Bekenstein-Hawking formula, we confirm the conjecture by Bianchi and Myers for this theory. Moreover, we calculate the first subleading term to entanglement entropy and show they agree with the Wald entropy up to extrinsic curvature terms.

http://arxiv.org/abs/1403.1393
Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
Ali Mollabashi, Noburo Shiba, Tadashi Takayanagi
(Submitted on 6 Mar 2014)
In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting N=4 super Yang-Mills theories by introducing a minimal surface in the S5 direction, instead of the AdS5 direction. This offers a possible generalization of holographic entanglement entropy.