This workshop is dedicated to the memory of Jacob Bekenstein (May 1, 1947  August 16, 2015.)
A pathfinder who never stopped looking for new horizons,
This workshop is dedicated to the memory of Jacob Bekenstein (May 1, 1947  August 16, 2015.)
A pathfinder who never stopped looking for new horizons,
Monday, August 17, 2015
Time 
Event 
Location 
8:30 – 9:00am 
Registration 
Reception 
9:00 – 9:05am 
Welcome and Opening Remarks 
Bob Room 

Chair 
Bob Room 
9:05 – 10:00am 
Tadashi Takayanagi, Yukawa Institute for Theoretical Physics, 
Bob Room 
10:00 – 11:00am 
Coffee Break 
Bistro – 1^{st} Floor 
11:00 – 12:00pm 
Matthew Headrick, Brandeis University 
Bob Room 
12:00 – 2:00pm 
Lunch 
Bistro – 2^{nd} Floor 

Chair 
Bob Room 
2:00 – 3:00pm 
Thomas Faulkner, University of Illinois 
Bob Room 
3:00 – 4:00pm 
Coffee Break 
Bistro – 1^{st} Floor 
4:00 – 5:00pm 
Veronika Hubeny, Durham University 
Bob Room 
5:00 – 5:30pm 
Jonathan Oppenheim, University College London 
Bob Room 
Tuesday,August 18, 2015
Time 
Event 
Location 

Chair 

9:00 – 10:00am 
Glen Evenbly, California Institute of Technology 
Bob Room 
10:00 – 11:00am 
Coffee Break 
Bistro – 1^{st} Floor 
11:00 – 12:00pm 
Jutho Haegemann, University of Ghent 
Bob Room 
12:00 – 2:00pm 
Lunch 
Bistro – 2^{nd} Floor 

Chair 
Bob Room 
2:00 – 3:00pm 
Fernando Pastawski, California Institute of Technology 
Bob Room 
3:00 – 4:00pm 
Coffee Break 
Bistro – 1^{st} Floor 
4:00 – 4:30pm 
Ning Bao, California Institute of Technology 
Bob Room 
4:30 – 5:00pm 
Mark Mezei, Princeton University 
Bob Room 
5:00 – 5:30pm 
Beni Yoshida, California Institute of Technology 
Bob Room 
Wednesday, August 19, 2015
Time 
Event 
Location 

Chair 
Bob Room 
9:00 – 10:00am 
Horacio Casini, Centro Atomico Bariloche 
Bob Room 
10:00 – 11:00am 
Coffee Break 
Bistro – 1^{st} Floor 
11:00 – 12:00pm 
Aron Wall, Institute for Advanced Study 
Bob Room 
12:00 – 12:10pm 
Conference Photo 
TBA 
12:10 – 2:00pm 
Lunch 
Bistro – 2^{nd} Floor 

Chair 
Bob Room 
2:00 – 3:00pm 
Ted Jacobson, University of Maryland 
Bob Room 
3:00 – 4:00pm 
Coffee Break 
Bistro – 1^{st} Floor 
4:00  4:30pm 
Aitor Lewkowycz, Princeton University 

4:30 – 5:00pm 
Gong Show: 
Bob Room 
5:00 – 5:30pm 
Poster Session Viewing: 
Atrium 
6:00pm onwards 
BBQ 
Bistro – 1^{st} Floor 
Thursday, August 20, 2015
Time 
Event 
Location 

Chair 
Bob Room 
9:00 – 10:00am 
James Sully, Stanford University 
Bob Room 
10:00 – 11:00am 
Coffee Break 
Bistro – 1^{st} Floor 
11:00 – 12:00pm 
Bartek Czech, Stanford University 
Bob Room 
12:00 – 2:00pm 
Lunch 
Bistro – 2^{nd} Floor 

Chair 
Bob Room 
2:00 – 3:00pm 
XiaoLiang Qi, Stanford University 
Bob Room 
3:00 – 4:00pm 
Coffee Break 
Bistro – 1^{st} Floor 
4:00 – 4:30pm 
Michal Heller, Perimeter Institute 
Bob Room 
4:30 – 5:00pm 
William Donnelly, University of California, Santa Barbara 
Bob Room 
5:00 – 5:30pm 
Subir Sachdev, Harvard University 
Bob Room 
Friday, August 21 2015
Time 
Event 
Location 

Chair 
Bob Room 
9:00 – 10:00am 
Adam Brown, Stanford University 
Bob Room 
10:00 – 11:00am 
Coffee Break 
Bistro – 1^{st} Floor 
11:00 – 12:00pm 
Nima Lashkari, Massachusetts Institute of Technology 
Bob Room 
12:00 – 2:00pm 
Lunch 
Bistro – 2^{nd} Floor 

Chair 

2:00 – 3:00pm 
Bianca Dittrich, Perimeter Institute 
Bob Room 
3:00 – 4:00pm 
Coffee Break 
Bistro – 1^{st} Floor 
4:00 – 5:00pm 
Mukund Rangamani, University of Durham 
Bob Room 
Ning Bao, California Institute of Technology
The Holographic Entropy Cone
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the RyuTakayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of RyuTakayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
Alessio Belenchia, SISSA
Analogue Gravity
Adam Brown, Stanford University
Wormholes and Complexity
I will discuss the connection between wormholes, action, computation and complexity.
Horacio Casini, Centro Atomico Bariloche
Area terms in entanglement entropy
We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the AdlerZee sum rule for the renormalization of the Newton constant in terms of correlator of traces of the stress tensor. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We check the sum rule holographicaly. We also discuss an application to the Ftheorem.
Aidan ChatwinDavies, California Institute of Technology
Consistency Conditions for an AdSMERA Correspondence
Bartek Czech, Standford University
Quotients of MERA
Bianca Dittrich, Perimeter Institute
3D Holography: from discretum to continuum
William Donnelly, University of California, Santa Barbara
Diffeomorphisminvariant observables and nonlocality
In a theory of gravity, observables must be diffeomorphisminvariant. Such observables are nonlocal, in contrast with the usual formulation of local quantum field theory. Working to leading order in Newtons constant G, I'll describe a construction of diffeomorphisminvariant observables for a scalar field coupled to gravity that closely parallels an analogous construction for charged particles in electrodynamics. These observables acting on the vacuum create scalar particles together with their (linearized) gravitational dressing. The commutator of two such spacelikeseparated observables is nonvanishing at order G, and is related to the gravitational potential between two masses.
Based on arXiv:1507.07921 with Steve Giddings.
Glen Evenbly, California Institute of Technology
Tensor Network Renormalization and the MERA
I describe a class of nonperturbative renormalization group (RG) transformations which, when applied to the (discrete time) Euclidean path integrals of a quantum systems on the lattice, can give results consistent with conformal transformations of quantum field theories. In particular, this class of transformation, which we call Tensor Network Renormalization (TNR), is shown to generate a scaleinvariant RG flow for quantum systems at a critical point. Applications of TNR towards study of quantum critical systems, and its relationship to the multiscaleentanglement renormalization ansatz (MERA) for ground and thermal states of quantum systems, will be discussed.
Thomas Faulkner, University of Illinois
Universal holographic description of CFT entanglement entropy
The RyuTakayanagi proposal (and generalizations) for holographic entanglement makes predictions for geometric CFT entanglement entropy (EE) that continue to hold for any CFT, regardless of existence of largeN limit or strong coupling. We establish this using a direct field theory calculation, thus providing a nontrivial check of the holographic proposal. This universality emerges for small perturbations of the EE of a ball shaped region. Einstein’s equations arise from the field theory calculation as a way to efficiently encode this perturbative CFT entanglement holographically in the geometry of a dual spacetime.
Jutho Haegeman, University of Ghent
Entanglement renormalization for quantum fields
The Multiscale Entanglement Renormalization Ansatz has proven to capture the ground state properties of strongly correlated quantum lattice systems, both in gapped regimes and at critical points, and realizes a lattice version of the holographic principle. In this talk, I will review a construction of entanglement renormalization that applies in the continuum (i.e. to quantum fields) and discuss several aspects such as the renormalization group equation and scaling exponents, illustrated using free field theories as example
Matthew Headrick, Brandeis University
A new perspective on holographic entanglement
We will present a reformulation of the RyuTakayanagi holographic entanglement entropy formula which does not involve the areas of surfaces. The reformulation leads to a picture of entanglement entropy of boundary regions being carried by Planckthickness "bit threads" in the bulk. We will argue that this picture resolves a number of conceptual difficulties surrounding the RT formula.
Michal Heller, Perimeter Institute
AdS/CFT Holography Integrability
Veronika Hubeny, Durham University
Geometric Constructs in AdS/CFT
Ted Jacobson, University of Maryland
Einstein's equation from maximal entropy of vacuum entanglement
If entanglement entropy in a small geodesic ball is maximized at fixed volume in the vacuum, then it should be stationary under variation to a nearby state. I will show that this stationarity condition is equivalent to the semiclassical Einstein equation. If the matter QFT is not conformal, then the derivation requires a further assumption about QFT, whose validity is currently under investigation. [Based on http://arxiv.org/abs/1505.04753]
Nima Lashkari, Massachusetts Institute of Technology
Quantum Fisher metric in field theory and gravity
In the first part of this talk, we discuss a generalized replica trick that is based on replica symmetry breaking partitions. This allows us compute the modular Hamiltonian, relative entropy and quantum Fisher information of excited states in conformal field theory.
In the second part, we consider holographic CFTs and show that quantum Fisher metric for ball shaped regions in vacuum is dual to the canonical energy of metric perturbations corresponding to the Rindler wedge of Antide Sitter space.
Aitor Lewkowycz, Princeton University
Towards a derivation of covariant holographic entanglement
Mark Mezei, Princeton University
Spread of entanglement and causality
We investigate causality constraints on the time evolution of entanglement entropy after a global quench. We analyze three models for the spread of entanglement: holographic quenches, the free particle streaming model of Calabrese and Cardy generalized to higher dimensions and an arbitrary pattern of entanglement, and a particle model with an infinite scattering rate. In these models we exhibit the intricate interplay of causality, strong subadditivity, and maximally entangled subsystems. Finally, using strong subadditivity we prove that the normalized rate of growth of entanglement entropy is bounded by the speed of light.
Jonathan Oppenheim, University College London
Do black holes create polyamory?
Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the nocloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or nonmonogamy, one needs to assume a tensor product structure between two points in spacetime that could instead be viewed as causally connected. In the latter case, one is violating the semiclassical causal structure of space, which is a strictly weaker implication than cloning or nonmonogamy. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system. A particular example of this is the HorowitzMaldacena proposal, and we argue that it needn't lead to cloning or violations of entanglement monogamy. In the case of the AMPS firewall experiment we find that the entanglement structure is modified, and one must have entanglement between the infalling Hawking partners and early time outgoing Hawking radiation which surprisingly tame violation of entanglement monogamy. http://arxiv.org/abs/1506.07133
Fernando Pastawski, California Institute of Technology
Holographic quantum errorcorrecting codes: Toy models for the bulk/boundary correspondence
In this talk I will introduce a family of exactly solvable toy models of a holographic correspondence based on a novel construction of quantum errorcorrecting codes with a tensor network structure. The building block for these models are a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is a quantum errorcorrecting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the holographic correspondence; in particular, the RyuTakayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. I will describe how bulk operators may be represented on the boundary regions mimicking the Rindlerwedge reconstruction.
XiaoLiang Qi, Stanford University
Holographic mapping, quantum error correction code and subAdS locality
In recent years, tensor networks have been proposed as a useful framework for understanding holographic duality, especially the relation between quantum entanglement and spacetime geometry. Most tensor networks studied so far are defined in the large scale compared with AdS radius. In this talk, I will describe a new tensor network approach which defines a holographic mapping that applies to a refined network with subAdS scale resolution, or even to a flat space. The idea of quantum error correction code plays an essential role in this approach. Using this new tensor network, we can study features of the bulk theory, such as how locality at subAdS scale emerges in a "low energy subspace" even though the whole theory is intrinsically nonlocal, as a quantum gravity theory should be.
Mukund Rangamani, University of Durham
Positivity, negativity, entanglement, and holography
Subir Sachdev, Harvard University
BekensteinHawking entropy and strange metals
Grant Salton, Standford University
Replicating Quantum Information in Spacetime
Tadashi Takayanagi, Yukawa Institute for Theoretical Physics, Kyoto University
Gravity Dual of Quantum Information Metric
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
Aron Wall, Institute for Advanced Study
Entropic Focussing
Beni Yoshida, California Institute of Technology
Order parameter for chaos
The fact that a black hole is a fastscrambler is at the heart of black hole information paradoxes. It has been suggested that chaos can be diagnosed by using an outoftime correlation function, which is closely related to the commutator of operators separated in time. In this talk I propose that the tripartite information (also known as topological entanglement entropy) can be used as a quantitative information theoretic measure of chaos. By viewing a quantum channel as a state via the ChoiJamilkowski isomorphism, the tripartite information measures fourparty entanglement between the “past” and the “future”, much like an outoftime correlation function. I will compute the timeevolution of the tripartite information for three systems; (a) nonintegrable spin systems on a lattice, (b) planar networks of perfect tensors which mimic the growth of the EinsteinRosen bridge and (c) a holographic system. This talk is based on an ongoing work with Xiaoliang Qi and Daniel Roberts.
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In this talk I will introduce a family of exactly solvable toy models of a holographic correspondence based on a novel construction of quantum errorcorrecting codes with a tensor network structure. The building block for these models are a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is a quantum errorcorrecting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively.
Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the nocloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or nonmonogamy, one needs to assume a tensor product structure between two points in spacetime that could instead be viewed as causally connected.
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Scientific Organizers: