# Condensed matter physics, area laws & LQG?

1. Sep 14, 2016

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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.

2. Sep 14, 2016

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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.

3. Sep 16, 2016

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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.

4. Sep 20, 2016

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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.

5. Sep 22, 2016

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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.

6. Oct 5, 2016

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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).

7. Oct 7, 2016

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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.

8. Oct 28, 2016

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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.

9. Nov 8, 2016

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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.

10. Nov 10, 2016

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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.

11. Nov 14, 2016

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https://arxiv.org/abs/1611.00360
de Sitter as a Resonance
Jonathan Maltz, Leonard Susskind
(Submitted on 1 Nov 2016)
A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory. In this paper we conjecture a potentially rigorous framework in which the status of de Sitter space is the same as that of a resonance in a scattering process. We conjecture that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant poles characteristic meta-stable intermediate states. A calculation employing constrained instantons illustrates this idea.

https://arxiv.org/abs/1611.03491
de Sitter Harmonies: Cosmological Spacetimes as Resonances
Jonathan Maltz
(Submitted on 10 Nov 2016)
The aim of this work is to provided the details of a calculation summarized in the recent paper by Maltz and Susskind which conjectured a potentially rigorous framework where the status of de Sitter space is the same as that of a resonance in a scattering process. The conjecture being that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant poles characteristic meta-stable intermediate states. A calculation employing constrained instantons is presented that illustrates this idea.

12. Nov 28, 2016

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https://arxiv.org/abs/1611.08581
Towards a dS/MERA correspondence
Raj Sinai Kunkolienkar, Kinjal Banerjee
(Submitted on 25 Nov 2016)
Recent advances have suggested that spacetime itself emerges from the entanglement of the quantum degrees of freedom living on the boundary. In the case of the AdS spacetimes, a particular class of tensor networks has been shown to realize the same via Multi-Scale Entanglement Renormalization Ansatz (MERA). In this paper we suggest a prescription for the dS/MERA correspondence and recover a discrete version of de Sitter Penrose diagram by using the MERA on conformal theories identified with the future/past conformal boundaries of the de Sitter spacetime. As anticipated, time appears as the emergent direction. We comment on the possible interpretation that the de Sitter cosmological horizon entropy involves entanglement with degrees of freedom across the cosmological horizon as well as the implications of our construction for cosmology.

https://arxiv.org/abs/1611.08613
Tensor Network Models of Unitary Black Hole Evaporation
Samuel Leutheusser, Mark Van Raamsdonk
(Submitted on 25 Nov 2016)
We introduce a general class of toy models to study the quantum information-theoretic properties of black hole radiation. The models are governed by a set of isometries that specify how microstates of the black hole at a given energy evolve to entangled states of a tensor product black-hole/radiation Hilbert space. The final state of the black hole radiation is conveniently summarized by a tensor network built from these isometries. We introduce a set of quantities generalizing the Renyi entropies that provide a complete set of bipartite/multipartite entanglement measures, and give a general formula for the average of these over initial black hole states in terms of the isometries defining the model. For models where the dimension of the final tensor product radiation Hilbert space is the same as that of the space of initial black hole microstates, the entanglement structure is universal, independent of the choice of isometries. In the more general case, we find that models which best capture the "information-free" property of black hole horizons are those whose isometries are tensors corresponding to states of tripartite systems with maximally mixed subsystems.

13. Dec 2, 2016

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https://arxiv.org/abs/1612.00433
Dean Carmi, Robert C. Myers, Pratik Rath
(Submitted on 1 Dec 2016)
We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary. We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice. The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest. We discuss possible implications arising from the geometric nature of these UV divergences.

14. Dec 9, 2016

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https://arxiv.org/abs/1612.02427
cMERA for Interacting Fields
Jordan S. Cotler, Javier Molina-Vilaplana, Mark T. Mueller
(Submitted on 7 Dec 2016)
We upgrade cMERA to a systematic variational ansatz and develop techniques for its application to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian Effective Potential, we can exactly solve for a variational approximation to the cMERA entangler. As examples, we treat scalar $φ^{4}$ theory and the Gross-Neveu model and extract non-perturbative behavior. We also comment on the connection between generalized squeezed coherent states and more generic entanglers.

15. Dec 19, 2016

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https://arxiv.org/abs/1612.05698
A defect in holographic interpretations of tensor networks
Bartlomiej Czech, Phuc H. Nguyen, Sivaramakrishnan Swaminathan
(Submitted on 17 Dec 2016)
We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.

16. Jan 1, 2017

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https://arxiv.org/abs/1612.09513
Holographic Bell Inequality
Jiunn-Wei Chen, Sichun Sun, Yun-Long Zhang
(Submitted on 30 Dec 2016)
We study the Bell inequality in a holographic model of a casually disconnected Einstein-Podolsky-Rosen (EPR) pair. The CHSH form of Bell inequality are computed using holographic Schwinger-Keldysh(SK) correlators. We show that the manifestation of quantum entanglement in Bell inequality can be reproduced from the classical gravitation theory in the bulk, which lends support to the ER=EPR conjecture.

17. Jan 4, 2017

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https://arxiv.org/abs/1701.01107
The Second Law of Quantum Complexity
(Submitted on 4 Jan 2017)
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of K qubits, and the positional entropy of a related classical system with 2K degrees of freedom. We also argue that the kinetic entropy of the classical system is equivalent to the Kolmogorov complexity of the quantum Hamiltonian. We observe that the expected pattern of growth of the complexity of the quantum system parallels the growth of entropy of the classical system. We argue that the property of having less-than-maximal complexity (uncomplexity) is a resource that can be expended to perform directed quantum computation.
Although this paper is not primarily about black holes, we find a surprising interpretation of the uncomplexity-resource as the accessible volume of spacetime behind a black hole horizon.

18. Jan 7, 2017

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https://arxiv.org/abs/1701.01383
Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
Goffredo Chirco, Daniele Oriti, Mingyi Zhang
(Submitted on 5 Jan 2017)
We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the R\'{e}nyi entropy of such states and recover the Ryu-Takayanagi formula, in three different cases corresponding to three different truncations/approximations, suggested by the established correspondence.

19. Jan 11, 2017

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https://arxiv.org/abs/1701.02319
Connecting Fisher information to bulk entanglement in holography
Souvik Banerjee, Johanna Erdmenger, Debajyoti Sarkar
(Submitted on 9 Jan 2017)
In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.

20. Mar 13, 2017

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https://arxiv.org/abs/1703.03483
Which quantum states are dual to classical spacetimes?
Marcelo Botta-Cantcheff, Pedro J. Martínez
(Submitted on 9 Mar 2017)
It is commonly accepted that states in a conformal field theory correspond to classical spacetimes with Anti-de-Sitter asymptotics. In this essay, we argue that such states should be coherent in the large-N limit, and show implications in the spacetime emergence mechanism. In particular, we argue that the microstates that compose a black hole (entangled) state in the Van Raamsdonk description cannot be interpreted as classical geometric configurations. Therefore, the conclusion is that care should be taken to interpret (micro)states in the gravity side, and that quantum coherence plays an important role in the description of the holographic emergence phenomenon.

https://arxiv.org/abs/1703.01519
Bulk reconstruction and the Hartle-Hawking wavefunction
Daniel Louis Jafferis
(Submitted on 4 Mar 2017)
In this work, a relation is found between state dependence of bulk observables in the gauge/gravity correspondence and nonperturbative diffeomorphism invariance. Certain bulk constraints, such as the black hole information paradox, appear to obstruct the existence of a linear map from bulk operators to exact CFT operators that is valid over the entire expected range of validity of the bulk effective theory. By formulating the bulk gravitational physics in the Hartle-Hawking framework to address these nonperturbative IR questions, I will demonstrate, in the context of eternal AdS-Schwarzschild, that the problematic operators fail to satisfy the Hamiltonian constraints nonperturbatively. In this way, the map between bulk effective theory Hartle-Hawking wavefunctions and exact CFT states can be linear on the full Hilbert space.

21. Apr 20, 2017

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https://arxiv.org/abs/1704.05464
Bulk locality from modular flow
Thomas Faulkner, Aitor Lewkowycz
(Submitted on 18 Apr 2017)
We study the reconstruction of bulk operators in the entanglement wedge in terms of low energy operators localized in the respective boundary region. To leading order in N, the dual boundary operators are constructed from the modular flow of single trace operators in the boundary subregion. The appearance of modular evolved boundary operators can be understood due to the equality between bulk and boundary modular flows and explicit formulas for bulk operators can be found with a complete understanding of the action of bulk modular flow, a difficult but in principle solvable task. We also obtain an expression when the bulk operator is located on the Ryu-Takayanagi surface which only depends on the bulk to boundary correlator and does not require the explicit use of bulk modular flow. This expression generalizes the geodesic operator/OPE block dictionary to general states and boundary regions.

https://arxiv.org/abs/1704.05839
High Energy Physics - Theory
Entanglement Wedge Reconstruction via Universal Recovery Channels

Jordan Cotler, Patrick Hayden, Grant Salton, Brian Swingle, Michael Walter
(Submitted on 19 Apr 2017)
We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that the algebraic consequences of exact equality can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. We illustrate the application of our formula in the 2+1 dimensional AdS-Rindler case, finding that it expresses local bulk operators in the AdS-Rindler wedge in terms of field operators corresponding to Rindler modes in its boundary domain of dependence. To reach these conclusions, we extend the theory of universal recovery channels to finite dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra.

22. May 2, 2017

### Denis

I would like to understand what is (possibly) wrong with the following approach to chiral fermions: First of all, the problem is not the fermions, anyway we have only massive Dirac fermions in the SM, and to put them on the lattice givens only a doubling problem. So, the only problem is a chiral gauge action. For vector gauge fields, we have Wilson lattice gauge field, which have exact gauge symmetry even on the lattice. But there is nothing with such exact gauge symmetry for chiral gauge action.

But why not simply using some inexact gauge symmetry? The result would be what? A mass of the gauge fields. But so what, given that weak gauge fields are massive in nature too, and the only part of electroweak gauge group which has zero mass is yet another vector gauge action.

I have been told massive gauge fields are non-renormalizable. But so what if the SM is anyway only an effective field theory? It means, in the large distance limit it gives results equivalent to some renormalizable theory, like that with exact gauge symmetry and a Higgs or so. So, what would be wrong with a lattice gauge theory which does not have exact gauge symmetry?

23. May 8, 2017

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https://arxiv.org/abs/1705.01964
Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
Muxin Han, Shilin Huang
(Submitted on 4 May 2017)
In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ⟩ using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement R\'enyi entropy of |Ψ⟩ is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting R\'enyi entropy Sn of |Ψ⟩ approximates with high precision the R\'enyi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate CFT ground state.

24. May 9, 2017

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https://arxiv.org/abs/1705.03048
De Finetti theorems and entanglement in large-N theories and gravity
Javier M. Magan
(Submitted on 8 May 2017)
The de Finetti theorem and its extensions concern the structure of multipartite probability distributions with certain symmetry properties, the paradigmatic original example being permutation symmetry. These theorems assert that such symmetric distributions are well approximated by convex combinations of uncorrelated ones. In this article, we apply de Finetti theorems to quantum gravity theories, such as the Sachdev-Ye-Kitaev (SYK) model or large-N vector and gauge theories. For SYK we put recent studies of information/entanglement dynamics in a general and rigorous basis. For vector and gauge theories, we find a gauge invariant operator whose expectation value provides the leading term in the entanglement entropy in all states close enough to a given classical state. These results can be unified through a generic statement about the nature of Schmidt decompositions and decoherence in large-N theories. In the reverse direction, we extend de Finetti theorems in various ways and provide an independent approach to the theorems only based on the large-N properties of the gauge invariant coherence group.

https://arxiv.org/abs/1705.03026
Nonlinear Gravity from Entanglement in Conformal Field Theories
Thomas Faulkner, Felix M. Haehl, Eliot Hijano, Onkar Parrikar, Charles Rabideau, Mark Van Raamsdonk
(Submitted on 8 May 2017)
In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu-Takayanagi formula) by an asymptotically AdS geometry. We show that such a geometry necessarily satisfies Einstein's equations perturbatively up to second order, with a stress energy tensor arising from matter fields associated with the sourced primary operators. We make no assumptions about AdS/CFT duality, so our work serves as both a consistency check for the AdS/CFT correspondence and a direct demonstration that spacetime and gravitational physics can emerge from the description of entanglement in conformal field theories.

25. May 12, 2017