Condensed matter physics, area laws & LQG?

[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.

 

[atyy]

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

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

 

[atyy]

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

 

[atyy]

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

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

 

[marcus]

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

 

[atyy]

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

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

 

[atyy]

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

 

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

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

 

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

 

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

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

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

 

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

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