Condensed matter physics, area laws & LQG?

[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.

 

[atyy]

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.

 

[torsten]

I know that it is maybe not very serious to propose my own work. But it has to do with the reversed process of entanglement known as decoherence. The quantum state in our theory is geometrically a wild embedding.

http://arxiv.org/abs/1309.7206
Decoherence in quantum cosmology and the cosmological constant
T. Asselmeyer-Maluga, J. Krol We discuss a spacetime having the topology of S3×R but with a different smoothness structure. The initial state of the cosmos in our model is identified with a wildly embedded 3-sphere (or a fractal space). In previous work we showed that a wild embedding is obtained by a quantization of a usual (or tame) embedding. Then a wild embedding can be identified with a (geometrical) quantum state. During a decoherence process this wild 3-sphere is changed to a homology 3-sphere. We are able to calculate the decoherence time for this process. After the formation of the homology 3-sphere, we obtain a spacetime with an accelerated expansion enforced by a cosmological constant. The calculation of this cosmological constant gives a qualitative agreement with the current measured value.

 

[torsten]

Also interesting in the context of a relation between condensed matter physics and gravity:

http://arxiv.org/abs/gr-qc/0410029
From Ginzburg-Landau to Hilbert-Einstein via Yamabe
Arkady L.Kholodenko, Ethan E.Ballard

In this work, based on some mathematical results obtained by Yamabe, Osgood, Phillips and Sarnak, we demonstrate that in dimensions three and higher the famous Ginzburg-Landau equations used in theory of phase transitions can be obtained (without any approximations) by minimization of the Riemannian-type Hilbert-Einstein action functional for pure gravity in the presence of cosmological term. We use this observation in order to bring to completion the work by Lifshitz (done in 1941) on group-theoretical refinements of the Landau theory of phase transitions. In addition, this observation allows us to develop a systematic extension to higher dimensions of known string-theoretic path integral methods developed for calculation of observables in two dimensional conformal field theories.

 

[atyy]

http://arxiv.org/abs/1403.3416
Holographic Holes in Higher Dimensions
Robert C. Myers, Junjie Rao, Sotaro Sugishita
(Submitted on 13 Mar 2014)
We extend the holographic construction from AdS3 to higher dimensions. In particular, we show that the Bekenstein-Hawking entropy of codimension-two surfaces in the bulk with planar symmetry can be evaluated in terms of the 'differential entropy' in the boundary theory. The differential entropy is a certain quantity constructed from the entanglement entropies associated with a family of regions covering a Cauchy surface in the boundary geometry. We demonstrate that a similar construction based on causal holographic information fails in higher dimensions, as it typically yields divergent results. We also show that our construction extends to holographic backgrounds other than AdS spacetime and can accommodate Lovelock theories of higher curvature gravity.

http://arxiv.org/abs/1403.3420
The Super BMS Algebra, Scattering and Holography
T. Banks
(Submitted on 13 Mar 2014)
I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras generalize the Fock space of massless particles. The algebra is realized in terms of operator valued measures on the momentum space dual to null infinity, and particles correspond to smearing these measures with delta functions. I conjecture that scattering amplitudes defined in terms of characteristic measures on finite spherical caps, the analog of Sterman-Weinberg jets[2], will have no infrared (IR) divergences. An important role is played by singular functions concentrated at zero momentum, and I argue that the formalism of Holographic Space- Time is the appropriate regulator for the singularities. It involves a choice of a time-like trajectory in Minkowski space. The condition that physics be independent of this choice of trajectory is a strong constraint on the scattering matrix. Poincare invariance of S is a particular consequence of this constraint. I briefly sketch the modifications of the formalism, which are necessary for dealing with massive particles. I also sketch how it should generalize to AdS space-time, and in particular show that the fuzzy spinor cutoff of HST implements the UV/IR correspondence of AdS/CFT.

 

[atyy]

http://arxiv.org/abs/1403.5395
Entanglement, Tensor Networks and Black Hole Horizons
Javier Molina-Vilaplana, Javier Prior
(Submitted on 21 Mar 2014)
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum quench are also analyzed. To this end, a full tensor network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a tensor network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the tensor network through a notion of distance within the network which emerges from its entanglement distribution.

 

[atyy]

The paper by Biachi and Smerlak was posted by marcus in his bibliography https://www.physicsforums.com/showpost.php?p=4707859&postcount=2154.

http://arxiv.org/abs/1404.0602
Entanglement entropy and negative-energy fluxes in two-dimensional spacetimes
Eugenio Bianchi, Matteo Smerlak
(Submitted on 2 Apr 2014 (v1), last revised 7 Apr 2014 (this version, v2))
It is well known that quantum effects can violate the positive energy conditions, if only for a limited time. Here we show in the context of two-dimensional conformal field theory that such violations are generic, and can be related to the entanglement structure of the conformal vacuum. Specifically, we prove that the renormalized energy flux F and entanglement entropy S at future null infinity satisfy ∫I+dλF(λ)exp[6S(λ)/c]=0, where c is the central charge (c=1 for the free scalar). When applied to unitary black hole evaporation, this identity implies that the semiclassical retarded mass (classical ADM mass minus vacuum outgoing energy) cannot be monotonically decreasing.

http://arxiv.org/abs/1404.1391
Notes on Entanglement in Abelian Gauge Theories
Djordje Radicevic
(Submitted on 4 Apr 2014)
We streamline and generalize the recent progress in understanding entanglement between spatial regions in Abelian gauge theories. We provide an unambiguous and explicit prescription for calculating entanglement entropy in a ZN lattice gauge theory. The main idea is that the lattice should be split into two disjoint regions of links separated by a buffer zone of plaquettes. We show that the previous calculations of the entanglement entropy can be realized as special cases of our setup, and we argue that the ambiguities reported in the previous work can be understood as basis choices for gauge-invariant operators living in the buffer zone. The proposed procedure applies to Abelian theories with matter and with continuous symmetry groups, both on the lattice and in the continuum.

 

[atyy]

http://arxiv.org/abs/1404.2634
Lattice Gerbe Theory
Arthur E. Lipstein, Ronald A. Reid-Edwards
(Submitted on 9 Apr 2014)
We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be U(1), the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also propose a very simple and natural non-abelian generalization with gauge group U(N)×U(N), which gives rise to U(N) Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.

 

[atyy]

http://arxiv.org/abs/1404.5419
On holographic entanglement entropy of non-local field theories
Da-Wei Pang
(Submitted on 22 Apr 2014)
We study holographic entanglement entropy of non-local field theories both at extremality and finite temperature. The gravity duals, constructed in arXiv:1208.3469 [hep-th], are characterized by a parameter w. Both the zero temperature backgrounds and the finite temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples with the entangling regions being a strip and a sphere. We find that the leading order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading order result is universal. For the finite temperature case we obtain the analytic expressions both in the high temperature limit and in the low temperature limit. In the former case the leading order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when w=1.

 

[atyy]

http://arxiv.org/abs/1404.5982
Holographic Heat Engines
Clifford V. Johnson
(Submitted on 23 Apr 2014)
It is shown that in theories of gravity where the cosmological constant is considered a thermodynamic variable, it is natural to use black holes as heat engines. Two examples are presented in detail using AdS charged black holes as the working substance. We notice that for static black holes, the maximally efficient traditional Carnot engine is also a Stirling engine. The case of negative cosmological constant supplies a natural realization of these engines in terms of the field theory description of the fluids to which they are holographically dual. We first propose a precise picture of how the traditional thermodynamic dictionary of holography is extended when the cosmological constant is dynamical and then conjecture that the engine cycles can be performed by using renormalization group flow. We speculate about the existence of a natural dual field theory counterpart to the gravitational thermodynamic volume.

http://arxiv.org/abs/1404.6198
Black Holes, Entanglement and Random Matrices
Vijay Balasubramanian, Micha Berkooz, Simon F. Ross, Joan Simon
(Submitted on 24 Apr 2014)
We provide evidence that strong quantum entanglement between Hilbert spaces does not generically create semiclassical wormholes between the corresponding geometric regions in the context of the AdS/CFT correspondence. We propose a description of low-energy gravity probes as random operators on the space of black hole states. We use this description to compute correlators between the entangled systems, and argue that a wormhole can only exist if correlations are large. Conversely, we also argue that large correlations can exist in the manifest absence of a Lorentzian wormhole. Thus the strength of the entanglement cannot generically diagnose spacetime connectedness, without information on the spectral properties of the probing operators. Our random matrix picture of probes also provides suggestive insights into the problem of "seeing behind a horizon".

 

[atyy]

http://arxiv.org/abs/1405.2933
Universality of Gravity from Entanglement
Brian Swingle, Mark Van Raamsdonk
(Submitted on 12 May 2014)
The entanglement "first law" in conformal field theories relates the entanglement entropy for a ball-shaped region to an integral over the same region involving the expectation value of the CFT stress-energy tensor, for infinitesimal perturbations to the CFT vacuum state. In recent work, this was exploited at leading order in N in the context of large N holographic CFTs to show that any geometry dual to a perturbed CFT state must satisfy Einstein's equations linearized about pure AdS. In this note, we investigate the implications of the leading 1/N correction to the exact CFT result. We show that these corrections give rise to the source term for the gravitational equations: for semiclassical bulk states, the expectation value of the bulk stress-energy tensor appears as a source in the linearized equations. In particular, the CFT first law leads to Newton's Law of gravitation and the fact that all sources of stress-energy source the gravitational field. In our derivation, this universality of gravity comes directly from the universality of entanglement (the fact that all degrees of freedom in a subsystem contribute to entanglement entropy).

 

[atyy]

http://arxiv.org/abs/1405.3743
Nonlinear constraints on gravity from entanglement
Shamik Banerjee, Apratim Kaviraj, Aninda Sinha
(Submitted on 15 May 2014)
Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual. We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion. We show that the Einstein value satisfies the positivity condition while the multi-dimensional parameter space away from it gets constrained.

 

[atyy]

http://arxiv.org/abs/1405.3949
Quantum Gravity, Dynamical Phase Space and String Theory
Laurent Freidel, Robert G. Leigh, Djordje Minic
(Submitted on 15 May 2014)
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase space and in which space-time is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The space-time and momentum space dynamics, and thus dynamical phase space, is governed by a new version of the Renormalization Group.

 

[Physics Monkey]

Wow, our title was put in color!

Also, I was not aware of this work by Freidel et al. which looks quite interesting.

 

[atyy]

Wow, our title was put in color!

Also, I was not aware of this work by Freidel et al. which looks quite interesting.

Large but finite N of colours :)

 

[atyy]

http://arxiv.org/abs/1405.7056
CFT/Gravity Correspondence on the Isolated Horizon
Amit Ghosh, Daniele Pranzetti
(Submitted on 27 May 2014)
A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures.

http://arxiv.org/abs/1405.7287
Statistical and entanglement entropy for black holes in quantum geometry
Alejandro Perez
(Submitted on 28 May 2014)
We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.

 

[atyy]

http://arxiv.org/abs/1405.7365
Disrupting Entanglement of Black Holes
Stefan Leichenauer
We study entanglement in thermofield double states of strongly coupled CFTs by analyzing two-sided Reissner-Nordstrom solutions in AdS. The central object of study is the mutual information between a pair of regions, one on each asymptotic boundary of the black hole. For large regions the mutual information is positive and for small ones it vanishes; we compute the critical length scale, which goes to infinity for extremal black holes, of the transition. We also generalize the butterfly effect of Shenker and Stanford to a wide class of charged black holes, showing that mutual information is disrupted upon perturbing the system and waiting for a time of order logE/δE in units of the temperature. We conjecture that the parametric form of this timescale is universal.

 

[atyy]

http://arxiv.org/abs/1406.1471
Entanglement contour
Yangang Chen, Guifre Vidal
(Submitted on 5 Jun 2014)
In the context of characterizing the structure of quantum entanglement in many-body systems, we introduce the entanglement contour, a tool to identify which real-space degrees of freedom contribute, and how much, to the entanglement of a region A with the rest of the system B. The entanglement contour provides a complementary, more re?fined approach to characterizing entanglement than just considering the entanglement entropy between A and B, with several concrete advantages. We illustrate this in the context of ground states and quantum quenches in fermionic quadratic systems. For instance, in a quantum critical system in D=1 spatial dimensions, the entanglement contour allows us to determine the central charge of the underlying conformal field theory from just a single partition of the system into regions A and B, (using the entanglement entropy for the same task requires considering several partitions). In D≥2 dimensions, the entanglement contour can distinguish between gapped and gapless phases that obey a same boundary law for entanglement entropy. During a local or global quantum quench, the time-dependent contour provides a detailed account of the dynamics of entanglement, including propagating entanglement waves, which offers a microscopic explanation of the behavior of the entanglement entropy as a function of time.

 

[atyy]

http://arxiv.org/abs/1406.2663
Multiboundary Wormholes and Holographic Entanglement
Vijay Balasubramanian, Patrick Hayden, Alexander Maloney, Donald Marolf, Simon F. Ross
(Submitted on 10 Jun 2014)
The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti-de Sitter space-time. We consider entangled states in the n-fold tensor product of a 1+1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS_3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, in some regions of the moduli space the entanglement is almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between at least n-1 parties, and that the distillable entanglement between the asymptotic regions is at least (n+1)/2 partite.

Commentary by Motl: http://motls.blogspot.com/2014/06/entanglement-and-networks-of-wormholes.html

 

[atyy]

http://arxiv.org/abs/1312.6634
Ken Wilson -- The Early Years
R. Jackiw

"because Cornell was a good university, was out in the country and [had] a good folk dancing group."

"without ... introducing ideas which are physically misleading and mathematically absurd. ('interaction representation' and the 'adiabatic hypothesis')"

 

[kneemo]

There is a deeper connection that exists here. The mathematics involves higher motivic structures however. Stay tuned for an upcoming paper in October.

 

[atyy]

There is a deeper connection that exists here. The mathematics involves higher motivic structures however. Stay tuned for an upcoming paper in October.

While we are waiting, anything you can recommend that's like "Higher Motivic Structures for Dummies"?

 

[atyy]

http://arxiv.org/abs/1406.4545
Entropy on a null surface for interacting quantum field theories and the Bousso bound
Raphael Bousso, Horacio Casini, Zachary Fisher, Juan Maldacena
(Submitted on 17 Jun 2014)
We study the vacuum-subtracted von Neumann entropy of a segment on a null plane. We argue that for interacting quantum field theories in more than two dimensions, this entropy has a simple expression in terms of the expectation value of the null components of the stress tensor on the null interval. More explicitly $ΔS=2π∫dd−2y∫10dx+g(x+)⟨T++⟩$, where $g(x+)$ is a theory-dependent function. This function is constrained by general properties of quantum relative entropy. These constraints are enough to extend our recent free field proof of the quantum Bousso bound to the interacting case. This unusual expression for the entropy as the expectation value of an operator implies that the entropy is equal to the modular Hamiltonian, $ΔS=⟨ΔK⟩$, where K is the operator in the right hand side. We explain how this equality is compatible with a non-zero value for ΔS. Finally, we also compute explicitly the function $g(x+)$ for theories that have a gravity dual.

http://arxiv.org/abs/1406.4611
Covariant Residual Entropy
Veronika E. Hubeny
(Submitted on 18 Jun 2014)
A recently explored interesting quantity in AdS/CFT, dubbed 'residual entropy', characterizes the amount of collective ignorance associated with either boundary observers restricted to finite time duration, or bulk observers who lack access to a certain spacetime region. However, the previously-proposed expression for this quantity involving variation of boundary entanglement entropy (subsequently renamed to 'differential entropy') works only in a severely restrictive context. We explain the key limitations, arguing that in general, differential entropy does not correspond to residual entropy. Given that the concept of residual entropy as collective ignorance transcends these limitations, we identify two correspondingly robust, covariantly-defined constructs: a 'strip wedge' associated with boundary observers and a 'rim wedge' associated with bulk observers. These causal sets are well-defined in arbitrary time-dependent asymptotically AdS spacetimes in any number of dimensions. We discuss their relation, specifying a criterion for when these two constructs coincide, and prove an inclusion relation for a general case. We also speculate about the implications for residual entropy. Curiously, despite each construct admitting a well-defined finite quantity related to the areas of associated bulk surfaces, these quantities are not in one-to-one correspondence with the defining regions of unknown. This has nontrivial implications about holographic measures of quantum information.

 

[kneemo]

While we are waiting, anything you can recommend that's like "Higher Motivic Structures for Dummies"?

This is a decent paper to start with:
Applied Motives overview

 

[atyy]

http://arxiv.org/abs/1406.4889
Holographic Reconstruction of General Bulk Surfaces
Bartlomiej Czech, Xi Dong, James Sully
(Submitted on 18 Jun 2014)
We propose a reconstruction of general bulk surfaces in any dimension in terms of the differential entropy in the boundary field theory. In particular, we extend the proof of Headrick et al. to calculate the area of a general class of surfaces, which have a 1-parameter foliation over a closed manifold. The area can be written in terms of extremal surfaces whose boundaries lie on ring-like regions in the field theory. We discuss when this construction has a description in terms of spatial entanglement entropy and suggest lessons for a more complete and covariant approach.

 

[atyy]

http://arxiv.org/abs/1406.5859
Entwinement and the emergence of spacetime
Vijay Balasubramanian, Borun D. Chowdhury, Bartlomiej Czech, Jan de Boer
(Submitted on 23 Jun 2014)
It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -- the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -- a 2d conformal field theory (CFT) that is dual to a conical defect in AdS3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.

 

[atyy]

http://arxiv.org/abs/1406.6989
Comments on Entanglement Negativity in Holographic Field Theories
Mukund Rangamani, Massimiliano Rota
(Submitted on 26 Jun 2014)
We explore entanglement negativity, a measure of the distillable entanglement contained in a quantum state, in relativistic field theories in various dimensions. We first give a general overview of negativity and its properties and then explain a well known result relating (logarithmic) negativity of pure quantum states to the Renyi entropy (at index 1/2), by exploiting the simple features of entanglement in thermal states. In particular, we show that the negativity of the thermofield double state is given by the free energy difference of the system at temperature T and 2T respectively. We then use this result to compute the negativity in the vacuum state of conformal field theories in various dimensions, utilizing results that have been derived for free and holographic CFTs in the literature. We also comment upon general lessons to be learned about negativity in holographic field theories.