Condensed matter physics, area laws & LQG?

[atyy]

.Scott started a discussion on an extremely interesting paper in https://www.physicsforums.com/threads/spectral-gap-or-gapless-undecidable.847554/

http://arxiv.org/abs/1502.04135
Undecidability of the Spectral Gap (short version)
Toby Cubitt, David Perez-Garcia, Michael M. Wolf
(Submitted on 13 Feb 2015)
The spectral gap -- the difference in energy between the ground state and the first excited state -- is one of the most important properties of a quantum many-body system. Quantum phase transitions occur when the spectral gap vanishes and the system becomes critical. Much of physics is concerned with understanding the phase diagrams of quantum systems, and some of the most challenging and long-standing open problems in theoretical physics concern the spectral gap, such as the Haldane conjecture that the Heisenberg chain is gapped for integer spin, proving existence of a gapped topological spin liquid phase, or the Yang-Mills gap conjecture (one of the Millennium Prize problems). These problems are all particular cases of the general spectral gap problem: Given a quantum many-body Hamiltonian, is the system it describes gapped or gapless?
Here we show that this problem is undecidable, in the same sense as the Halting Problem was proven to be undecidable by Turing. A consequence of this is that the spectral gap of certain quantum many-body Hamiltonians is not determined by the axioms of mathematics, much as Goedels incompleteness theorem implies that certain theorems are mathematically unprovable. We extend these results to prove undecidability of other low temperature properties, such as correlation functions. The proof hinges on simple quantum many-body models that exhibit highly unusual physics in the thermodynamic limit.

Comments: 8 pages, 3 figures. See long companion paper arXiv:1502.04573 (same title and authors) for full technical details

 

[marcus]

http://arxiv.org/abs/1512.04993
Complexity, Action, and Black Holes
Adam Brown, Daniel A. Roberts, Leonard Susskind, Brian Swingle, Ying Zhao
(Submitted on 15 Dec 2015)
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the `Wheeler-DeWitt' patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are fastest computers in nature.
Comments: 55+14 pages, many figures

 

[atyy]

http://arxiv.org/abs/1512.06206
Finite Entanglement Entropy of Black Holes
Stefano Giaccari, Leonardo Modesto, Leslaw Rachwal, Yiwei Zhu
(Submitted on 19 Dec 2015)
We compute the area term contribution to the black holes' entanglement entropy for a class of local or weakly nonlocal renormalizable gravitational theories coupled to matter. For the case of super-renormalizable theories, we can get a finite conical entropy expressed only in terms of the classical Newton constant either by completing the theory to a finite one in dimensional regularization or by removing the quadratic divergences in the cut-off regularization by the introduction of additional interaction terms. Therefore, our result is independent from the renormalization scheme. We also propose a theory in which the renormalization of the Newton constant is entirely due to the standard model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.

http://arxiv.org/abs/1512.06431
Relative entropy equals bulk relative entropy
Daniel L. Jafferis, Aitor Lewkowycz, Juan Maldacena, S. Josephine Suh
(Submitted on 20 Dec 2015)
We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

http://arxiv.org/abs/1512.06784
The 1/N expansion method in quantum field theory
H. Sazdjian
(Submitted on 16 Dec 2015)
The motivations of the 1/N expansion method in quantum field theory are explained. The method is first illustrated with the O(N) model of scalar fields. A second example is considered with the two-dimensional Gross-Neveu model of fermion fields with global U(N) and discrete chiral symmetries. The case of QCD is briefly sketched.

 

[atyy]

http://arxiv.org/abs/1601.05416
Bulk Reconstruction in the Entanglement Wedge in AdS/CFT
Xi Dong, Daniel Harlow, Aron C. Wall
(Submitted on 20 Jan 2016)
In this note we prove a simple theorem in quantum information theory, which implies that bulk operators in the Anti-de Sitter / Conformal Field Theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A, provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.

http://arxiv.org/abs/1601.05611
Asymmetric interiors for small black holes
Daniel Kabat, Gilad Lifschytz
(Submitted on 21 Jan 2016)
We develop the representation of infalling observers and bulk fields in the CFT as a way to understand the black hole interior in AdS. We first discuss properties of CFT states which are dual to black holes. Then we show that in the presence of a Killing horizon bulk fields can be decomposed into pieces we call ingoing and outgoing. The ingoing field admits a simple operator representation in the CFT, even inside a small black hole at late times, which leads to a simple CFT description of infalling geodesics. This means classical infalling observers will experience the classical geometry in the interior. The outgoing piece of the field is more subtle. In an eternal two-sided geometry it can be represented as an operator on the left CFT. In a stable one-sided geometry it can be described using entanglement via the PR construction. But in an evaporating black hole trans-horizon entanglement changes at the Page time, which means that for old black holes the PR construction fails and the outgoing field does not see local geometry. This picture of the interior allows the CFT to reconcile unitary Hawking evaporation with the classical experience of infalling observers.

 

[marcus]

http://arxiv.org/abs/1601.05707
Projective quantum states for Loop Quantum Gravity coupled to tensor fields
Andrzej Okolow
(Submitted on 21 Jan 2016)
We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity obtained by Lanery and Thiemann we construct quantum states for LQG coupled to tensor fields.
23 pages.
[Atyy, please let me know if this paper does not fit comfortably in your bibliography and I'll delete it]

 

[marcus]

http://arxiv.org/abs/1602.00106
A Note on Entanglement Entropy, Coherent States and Gravity
Madhavan Varadarajan
(Submitted on 30 Jan 2016)
The entanglement entropy of a free quantum field in a coherent state is independent of its stress energy content. We use this result to highlight the fact that while the Einstein equations for first order variations about a locally maximally symmetric vacuum state of geometry and quantum fields seem to follow from Jacobson's principle of maximal vacuum entanglement entropy, their possible derivation from this principle for the physically relevant case of finite but small variations remains an open issue. We also apply this result to the context of Bianchi's identification, independent of unknown Planck scale physics, of the first order variation of Bekenstein Hawking area with that of vacuum entanglement entropy. We argue that under certain technical assumptions this identification seems not to be extendible to the context of finite but small variations to coherent states. Our particular method of estimation of entanglement entropy variation reveals the existence of certain contributions over and above those appearing in Jacobson's and Bianchi's works. We discuss the sense in which these contributions may be subleading to those already present in these works.
15 pages

http://arxiv.org/abs/1602.03237
Can chaos be observed in quantum gravity?
Bianca Dittrich, Philipp A. Hoehn, Tim A. Koslowski, Mike I. Nelson
(Submitted on 10 Feb 2016)
Full general relativity is almost certainly non-integrable and likely chaotic and therefore almost certainly possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model it turns out that a refinement to a polymer-type topology, as e.g. used in loop quantum cosmology, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit.
4 pages + references

Atyy, please let me know if including the Dittrich et al here diverges from the main thread topic or if it should for any reason be deleted.

 

[atyy]

Atyy, please let me know if including the Dittrich et al here diverges from the main thread topic or if it should for any reason be deleted.

Everything Dittrich does is relevant to this thread - ok, maybe not brushing her teeth, but I'm sure that could be relevant too

 

[atyy]

http://arxiv.org/abs/1509.04507
The limits of Matrix Product State models
Miguel Navascues, Tamas Vertesi
(Submitted on 15 Sep 2015 (v1), last revised 25 Jan 2016 (this version, v2))
For the past twenty years, Tensor Network States (TNS) have been widely used to model the low energy sector of local Hamiltonians. Their success in doing so has led to the wide-held mantra that TNS of low bond dimension are the `only physical states' of natural condensed matter systems. However, given our experimental limitations to interact with such systems, it is not clear how this conjecture translates into any observable effect. In this Letter we give a first step in this direction by identifying particular operational features pertaining to all Matrix Product States (MPS), the class of TNS used to model non-critical one-dimensional spin chains. By exploiting two surprising structural constraints of MPS, we show how to systematically derive `bond dimension witnesses', or k-local operators whose expectation value allows us to lower bound the bond dimension of the underlying quantum state. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of MPS to: a) derive some limitations on the use of MPS and PEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.
Comments: New title, abstract and numerical results. We still do not acknowledge support from the European Research Council

 

[atyy]

http://arxiv.org/abs/1603.05250
A Holographic Entanglement Entropy Conjecture for General Spacetimes
Fabio Sanches, Sean J. Weinberg
(Submitted on 16 Mar 2016)
We present a natural generalization of holographic entanglement entropy proposals beyond the scope of AdS/CFT by anchoring extremal surfaces to holographic screens. Holographic screens are a natural extension of the AdS boundary to arbitrary spacetimes and are preferred codimension 1 surfaces from the viewpoint of the covariant entropy bound. Screens have a unique preferred foliation into codimension 2 surfaces called leaves. Our proposal is to find the areas of extremal surfaces achored to the boundaries of regions in leaves. We show that the properties of holographic screens are sufficient to prove, under generic conditions, that extremal surfaces anchored in this way always lie within a causal region associated with a given leaf. Within this causal region, a maximin construction similar to that of Wall proves that our proposed quantity satisfies standard properties of entanglement entropy like strong subadditivity. We conjecture that our prescription computes entanglement entropies in quantum states that holographically define arbitrary spacetimes, including those in a cosmological setting with no obvious boundary on which to anchor extremal surfaces.

 

[atyy]

http://arxiv.org/abs/1603.08509
Horizon as Critical Phenomenon
Sung-Sik Lee
(Submitted on 28 Mar 2016)
We show that renormalization group(RG) flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N) vector model in the large N limit based on the holographic dual constructed from quantum RG. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity : the depth of RG transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum RG.

 

[atyy]

http://arxiv.org/abs/1604.00354
Bit threads and holographic entanglement
Michael Freedman, Matthew Headrick
(Submitted on 1 Apr 2016)
The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, we invoke the notion of a "flow", defined as a divergenceless norm-bounded vector field, or equivalently a set of Planck-thickness "bit threads". The entanglement entropy of a boundary region is given by the maximum flux out of it of any flow, or equivalently the maximum number of bit threads that can emanate from it. The threads thus represent entanglement between points on the boundary, and naturally implement the holographic principle. As we explain, this new picture clarifies several conceptual puzzles surrounding the RT formula. We give flow-based proofs of strong subadditivity and related properties; unlike the ones based on minimal surfaces, these proofs correspond in a transparent manner to the properties' information-theoretic meanings. We also briefly discuss certain technical advantages that the flows offer over minimal surfaces. In a mathematical appendix, we review the max flow-min cut theorem on networks and on Riemannian manifolds, and prove in the network case that the set of max flows varies Lipshitz continuously in the network parameters.

http://arxiv.org/abs/1604.00388
Dynamics of the Area Law of Entanglement Entropy
Stefan Leichenauer, Mudassir Moosa, Michael Smolkin
(Submitted on 1 Apr 2016)
We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to the area law under the assumption that the field theory resides in a vacuum state when a small time-dependent perturbation of a relevant coupling constant is turned on. Using this formula, we carry out explicit calculations in free field theories deformed by a time dependent mass, whereas for a generic QFT we show that the time dependent first order correction is governed by the spectral function defining the two-point correlation function of the trace of the energy-momentum tensor. We also carry out holographic calculations based on the HRT proposal and find qualitative and, in certain cases, quantitative agreement with the field theory calculations.

 

[atyy]

http://arxiv.org/abs/1604.01772
EPR Pairs, Local Projections and Quantum Teleportation in Holography
Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi, Kento Watanabe
(Submitted on 6 Apr 2016)
In this paper we analyze three quantum operations in two dimensional conformal field theories (CFTs): local projection measurements, creations of partial entanglement between two CFTs, and swapping of subsystems between two CFTs. We also give their holographic duals and study time evolutions of entanglement entropy. By combining these operations, we present an analogue of quantum teleportation between two CFTs and give its holographic realization. We introduce a new quantity to probe tripartite entanglement by using local projection measurement.

 

[atyy]

http://arxiv.org/abs/1605.05751
A Holographic Dual of the Quantum Inequalities
Adam R. Levine
(Submitted on 18 May 2016)
In this note, we establish the 2-D Quantum Inequalities - first proved by Flanagan - for all CFTs with a causal holographic dual. Following the treatment of Kelly $\&$ Wall, we establish that the Boundary Causality Condition in an asymptotic AdS spacetime implies the Quantum Inequalities on the boundary. Our results extend easily to curved spacetime and are stable under deformations of the CFT by relevant operators. We discuss higher dimensional generalizations and possible connections to recent bounds on $a/c$ in 4-D CFTs.

 

[atyy]

http://arxiv.org/abs/1605.06166
Topology and geometry cannot be measured by an operator measurement in quantum gravity
David Berenstein, Alexandra Miller
(Submitted on 19 May 2016)
In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

 

[atyy]

http://arxiv.org/abs/1605.09396
Entanglement Entropy and Duality
Djordje Radicevic
(Submitted on 30 May 2016)
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.

 

[atyy]

http://arxiv.org/abs/1606.00621
Exploring the Tensor Networks/AdS Correspondence
Arpan Bhattacharyya, Zhe-Shen Gao, Ling-Yan Hung, Si-Nong Liu
(Submitted on 2 Jun 2016)
In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Study- ing generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admits generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

 

[atyy]

http://arxiv.org/abs/1606.01267
Holographic Space-time, Newton's Law and the Dynamics of Black Holes
Tom Banks, Willy Fischler
(Submitted on 3 Jun 2016)
We revisit the construction of models of quantum gravity in d dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton`s law. These same models also have emergent energy, momentum and angular conservation laws, despite being based on time dependent Hamiltonians. Many of the scattering amplitudes have a Feynman diagram like structure: local interaction vertices connected by propagation of free particles (really Sterman-Weinberg jets of particles). However, there are also amplitudes where jets collide to form large meta-stable objects, with all the scaling properties of black holes: energy, entropy and temperature, as well as the characteristic time scale for the decay of perturbations. We generalize the conjecture of Sekino and Susskind, to claim that all of these models are fast scramblers. The rationale for this claim is that the interactions are invariant under fuzzy subgroups of the group of volume preserving diffeomorphisms, so that they are highly non-local on the holographic screen. We review how this formalism resolves the Firewall Paradox.

 

[atyy]

http://arxiv.org/abs/1605.07768
Holographic fluctuations and the principle of minimal complexity
Wissam Chemissany, Tobias J. Osborne
(Submitted on 25 May 2016)
We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.

 

[atyy]

http://arxiv.org/abs/1606.04537
Linearity of Holographic Entanglement Entropy
Ahmed Almheiri, Xi Dong, Brian Swingle
(Submitted on 14 Jun 2016)
We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.

 

[atyy]

http://arxiv.org/abs/1606.04951
Precision lattice test of the gauge/gravity duality at large-N
Evan Berkowitz, Enrico Rinaldi, Masanori Hanada, Goro Ishiki, Shinji Shimasaki, Pavlos Vranas
(Submitted on 15 Jun 2016)
We pioneer a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-N and continuum limits of the gauge theory are taken for the first time at various temperatures 0.4≤T≤1.0. As a way to directly test the gauge/gravity duality conjecture we compute the internal energy of the black hole directly from the gauge theory and reproduce the coefficient of the supergravity result E/N2=7.41T14/5. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.

 

[atyy]

http://arxiv.org/abs/1605.05999
Thermal geometry from CFT at finite temperature
Wen-Cong Gan, Fu-Wen Shu, Meng-He Wu
(Submitted on 19 May 2016)
We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking-Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

http://arxiv.org/abs/1606.07628
Emergent geometry, thermal CFT and surface/state correspondence
Wen-Cong Gan, Fu-Wen Shu, Meng-He Wu
(Submitted on 24 Jun 2016)
We study a conjectured correspondence between any codimension two convex surface and a quantum state (SS-duality for short). By generalizing thermofield double formalism to continuum version of the multi-scale entanglement renormalization ansatz (cMERA) and using the SS-duality, we propose a general framework to emerge the thermal geometry from CFT at finite temperature. As an example, the case of 2d CFT is considered carefully. We calculate its information metric and show that it is the BTZ black hole or the thermal AdS as expectation.

 

[atyy]

http://arxiv.org/abs/1607.03510
Holographic Space-time Models of Anti-deSitter Space-times
Tom Banks, Willy Fischler
(Submitted on 12 Jul 2016)
We study the constraints on HST models of AdS space-time. The causal diamonds of HST along time-like geodesics of AdS space-time, fit nicely into the FRW patch of AdS space. The coordinate singularity of the FRW patch is identified with the proper time at which the Hilbert space of the causal diamond becomes infinite dimensional. For diamonds much smaller than the AdS radius, RAdS, the time dependent Hamiltonians of HST are the same as those used to describe similar diamonds in Minkowski space. In particular, they are invariant under the fuzzy analog of volume preserving diffeomorphisms of the holographic screen, which leads to fast scrambling of perturbations on the horizon of a black hole of size smaller than RAdS. We argue that, in order to take a limit of this system which converges to a CFT, one must choose Hamiltonians, in a range of proper times of order RAdS, which break this invariance, and become local in a particular choice of basis for the variables. We show that, beginning with flat, sub-RAdS, patches of dimension D, the resulting CFT, constructed from the variables of HST, is inconsistent with the entropy of large black holes, unless one has at least two compact dimensions, whose size is of order RAdS. The argument is connected to a new observation about the scrambling rate of information localized on the compact dimensions. Our construction explains why large AdS black holes do not have the fast scrambling property. Our present approach cannot deal with models where string theory is weakly coupled and RAdS is of order the string scale, because the relationship between area and entropy is non-universal in such models. On spatial length scales longer than RAdS, our mapping of HST variables into CFT shares much with the Tensor Network Renormalization Group (TNRG)[1] and is a sort of evolving error correcting code[2].

http://arxiv.org/abs/1607.03605
Explicit reconstruction of the entanglement wedge
Jung-Wook Kim
(Submitted on 13 Jul 2016)
The problem of bulk locality, or how the boundary encodes the bulk in AdS/CFT, is still a subject of study today. One of the major issues that needs more elucidation is the problem of subregion duality; what information of the bulk a given boundary subregion encodes. Although proofs given by two teams of researchers, Dong, Harlow, and Wall and Bao, and Kim, state that the entanglement wedge of the bulk should be reconstructible from boudnary subregions, no explicit procedure for reconstructing the entanglement wedge was as of yet given. In this paper, mode sum approach to obtaining smearing functions is generalised to include bulk reconstruction in the entanglement wedge of boundary subregions. It is generally expectated that solutions to the wave equation on a complicated coordinate patch are needed, but this hard problem has been transferred to a less hard but tractable problem of matrix inversion.

 

[atyy]

http://arxiv.org/abs/1607.03901
The Ryu-Takayanagi Formula from Quantum Error Correction
Daniel Harlow
(Submitted on 13 Jul 2016)
I argue that a version of the quantum-corrected Ryu-Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the final statement expressed in the language of operator-algebra quantum error correction. In AdS/CFT this gives a "purely boundary" interpretation of the formula. I also extend a recent theorem, which established entanglement-wedge reconstruction in AdS/CFT, when interpreted as a subsystem code, to the more general, and I argue more physical, case of subalgebra codes. For completeness, I include a self-contained presentation of the theory of von Neumann algebras on finite-dimensional Hilbert spaces, as well as the algebraic definition of entropy. The results confirm a close relationship between bulk gauge transformations, edge-modes/soft-hair on black holes, and the Ryu-Takayanagi formula. They also suggest a new perspective on the homology constraint, which basically is to get rid of it in a way that preserves the validity of the formula, but which removes any tension with the linearity of quantum mechanics. Moreover they suggest a boundary interpretation of the "bit threads" recently introduced by Freedman and Headrick.

 

[atyy]

http://arxiv.org/abs/1607.08881
Fusion basis for lattice gauge theory and loop quantum gravity
Clement Delcamp, Bianca Dittrich, Aldo Riello
(Submitted on 29 Jul 2016)
We introduce a new basis for the gauge--invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2+1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin--network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi--local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse--graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin--network basis, in which it is much more complicated to account for electric excitations, i.e. for Gau\ss~constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi--scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2+1) gravity coupled to point particles. In a follow--up work, we will exploit this notion to provide a new definition of entanglement entropy for these theories.

 

[atyy]

http://arxiv.org/abs/1608.02040
A Toy Model of Entwinement
Jennifer Lin
(Submitted on 5 Aug 2016)
Entwinement is the entanglement entropy of a subset of gauge-variant degrees of freedom in a certain twisted state of an orbifold CFT, defined by embedding the state in a larger Hilbert space with some gauge constraints removed. We propose an intrinsically gauge-invariant, algebraic definition of entwinement. Our main piece of evidence is a computation showing that, in a spin system that resembles the orbifold CFT, the analog of entwinement is the entanglement entropy of a gauge-invariant subalgebra, which we identify. We review why entwinement is relevant for the conjecture that entanglement builds spacetime.

 

[haushofer]

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

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

How is this reconcilable with holography? Holography is greatly motivated by the non-extensive nature of black hole entropy. Any thoughts?

 

[atyy]

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

 

[atyy]

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

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

How is this reconcilable with holography? Holography is greatly motivated by the non-extensive nature of black hole entropy. Any thoughts?

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

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

 

[haushofer]

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

 

[atyy]

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

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

 

[atyy]

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

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

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

 

[atyy]

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

 

[atyy]

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

 

[atyy]

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

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

 

[atyy]

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