Condensed matter physics, area laws & LQG?

[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.

 

[atyy]

http://arxiv.org/abs/1609.03560
Classical Holographic Codes
Enrico M. Brehm, Benedikt Richter
(Submitted on 12 Sep 2016)
In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.

http://arxiv.org/abs/1609.03651
Discussion of the Entanglement Entropy in Quantum Gravity
Chen-Te Ma
(Submitted on 13 Sep 2016)
Quantum gravity needs to be satisfied by the holographic principle, and the entanglement entropy already has holographic evidences via anti-de Sitter/ Conformal field theory correspondence. Thus, we explore principles of quantum gravity via the entanglement entropy. We compute the entanglement entropy in two dimensional Einstein-Hilbert action to understand quantum geometry and area law. Then we also discuss two dimensional conformal field theory because we expect strongly coupled conformal field theory can describe perturbative quantum gravity theory. We find universal terms of the entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval and some cases of multiple intervals. To extend our discussion to generic multiple intervals, we use a geometric method to determine the entanglement entropy. Finally, we argue translational invariance possibly be a necessary condition in quantum gravity theory from ruing out volume law of the entanglement entropy.

http://arxiv.org/abs/1609.03991
Entwinement in discretely gauged theories
V. Balasubramanian, A. Bernamonti, B. Craps, T. De Jonckheere, F. Galli
(Submitted on 13 Sep 2016)
We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an $S_{N}$ gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to $AdS_{3}$ at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M=0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.

 

[atyy]

http://arxiv.org/abs/1609.04036
The Black Hole Information Problem
Joseph Polchinski
(Submitted on 13 Sep 2016)
The black hole information problem has been a challenge since Hawking's original 1975 paper. It led to the discovery of AdS/CFT, which gave a partial resolution of the paradox. However, recent developments, in particular the firewall puzzle, show that there is much that we do not understand. I review the black hole, Hawking radiation, and the Page curve, and the classic form of the paradox. I discuss AdS/CFT as a partial resolution. I then discuss black hole complementarity and its limitations, leading to many proposals for different kinds of `drama.' I conclude with some recent ideas.

 

[atyy]

http://arxiv.org/abs/1609.04645
From Path Integrals to Tensor Networks for AdS/CFT
Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe
(Submitted on 15 Sep 2016)
In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient optimization by making its UV cut off position dependent and define a quantum state at each length scale. We conjecture that this path-integral corresponds to a time slice of AdS. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual 2d CFT. Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous MERA (cMERA). We also give a heuristic argument why we can expect a sub-AdS scale bulk locality for holographic CFTs.

http://arxiv.org/abs/1609.04806
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
Clement Delcamp, Bianca Dittrich, Aldo Riello
(Submitted on 15 Sep 2016)
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non--Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non--Abelian analogue of the `magnetic centre choice', as obtained through an extended--Hilbert--space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement theory can be related to a choice of (squeezed) vacuum state.

 

[atyy]

http://arxiv.org/abs/1609.05222
What prevents gravitational collapse in string theory?
Samir D. Mathur
(Submitted on 16 Sep 2016)
It is conventionally believed that if a ball of matter of mass M has a radius close to 2GM then it must collapse to a black hole. But string theory microstates (fuzzballs) have no horizon or singularity, and they do {\it not} collapse. We consider two simple examples from classical gravity to illustrate how this violation of our intuition happens. In each case the `matter' arises from an extra compact dimension, but the topology of this extra dimension is not trivial. The pressure and density of this matter diverge at various points, but this is only an artifact of dimensional reduction; thus we bypass results like Buchadahl's theorem. Such microstates give the entropy of black holes, so these topologically nontrivial constructions dominate the state space of quantum gravity.

 

[atyy]

http://arxiv.org/abs/1609.06439
Invitation to random tensors
Razvan Gurau
(Submitted on 21 Sep 2016)
Preface to the SIGMA special issue "Tensor Models, Formalism and Applications." The SIGMA special issue "Tensor Models, Formalism and Applications" is a collection of eight excellent, up to date reviews \cite{Ryan:2016sundry,Bonzom:2016dwy,Rivasseau:2016zco,Carrozza:2016vsq,Krajewski:2016svb,Rivasseau:2016rgt,Tanasa:2015uhr,Gielen:2016dss} on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field.
This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.

 

[atyy]

https://arxiv.org/abs/1610.00669
Bulk Locality and Entanglement Swapping in AdS/CFT
William R. Kelly
(Submitted on 3 Oct 2016)
Localized bulk excitations in AdS/CFT are produced by operators which modify the pattern of entanglement in the boundary state. We show that simple models--consisting of entanglement swapping operators acting on a qubit system or a free field theory--capture qualitative features of gravitational backreaction and reproduce predictions of the Ryu-Takayanagi formula. These entanglement swapping operators naturally admit multiple representations associated with different degrees of freedom, thereby reproducing the code subspace structure emphasized by Almheiri, Dong, and Harlow. We also show that the boundary Reeh-Schlieder theorem implies that equivalence of certain operators on a code subspace necessarily breaks down when non-perturbative effects are taken into account (as is expected based on bulk arguments).

 

[atyy]

https://arxiv.org/abs/1610.01719
Entanglement in a two-dimensional string theory
William Donnelly, Gabriel Wong
(Submitted on 6 Oct 2016)
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider entanglement entropy in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large $N$. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space, giving a precise state-counting interpretation to the entropy, including its leading $O(N^{2})$ piece. In the process we reinterpret the sphere partition function as a thermal ensemble of of open strings whose endpoints are anchored to an object at the entangling surface that we call an E-brane.

 

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https://arxiv.org/abs/1610.08516
Into the Bulk: A Covariant Approach
Netta Engelhardt
(Submitted on 26 Oct 2016)
I propose a general, covariant way of defining when one region is "deeper in the bulk" than another. This definition is formulated outside of an event horizon (or in the absence thereof) in generic geometries; it may be applied to both points and surfaces, and may be used to compare the depth of bulk points or surfaces relative to a particular boundary subregion or relative to the entire boundary. Using the recently proposed "lightcone cut" formalism, the comparative depth between two bulk points can be determined from the singularity structure of Lorentzian correlators in the dual field theory. I prove that, by this definition, causal wedges of progressively larger regions probe monotonically deeper in the bulk. The definition furthermore matches expectations in pure AdS and in static AdS black holes with isotropic spatial slices, where a well-defined holographic coordinate exists. In terms of holographic RG flow, this new definition of bulk depth makes contact with coarse-graining over both large distances and long time scales.

https://arxiv.org/abs/1610.08970
Boundary Fluctuations and A Reduction Entropy
Christopher Herzog, Kuo-Wei Huang
(Submitted on 27 Oct 2016)
The boundary Weyl anomalies live on a codimension-1 boundary, ∂M. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, Σ. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on ∂M to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.

 

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https://arxiv.org/abs/1611.02647
Multipartite Entanglement and Firewalls
Shengqiao Luo, Henry Stoltenberg, Andreas Albrecht
(Submitted on 8 Nov 2016)
Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a "firewall" inside the black hole horizon which prevents objects from falling smoothly toward the singularity. A fundamental limitation on the behavior of quantum entanglement known as "monogamy" plays a key role in the AMPS argument. Our goal is to study and apply many-body entanglement theory to consider the entanglement among different parts of Hawking radiation and black holes. Using the multipartite entanglement measure called negativity, we identify an example which could change the AMPS accounting of quantum entanglement and perhaps eliminate the need for a firewall. Specifically, we constructed a toy model for black hole decay which has different entanglement behavior than that assumed by AMPS. We discuss the additional steps that would be needed to bring lessons from our toy model to our understanding of realistic black holes.

 

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https://arxiv.org/abs/1611.02702
Toward a Holographic Theory for General Spacetimes
Yasunori Nomura, Nico Salzetta, Fabio Sanches, Sean J. Weinberg
(Submitted on 8 Nov 2016)
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct sum and "spacetime equals entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.