Quantum Information and String Theory 2019

Program

• 1st, 2nd week
• 3rd week (QI workshop)
• 4th, 5th weeks (IFQ school/workshop)

4th, 5th weeks (IFQ school/workshop)

Detailed Program (PDF) (updated on June 25).

Video of the lectures: Yoshida-1, Yoshida-2, Yoshida-3, Vidick-1, Vidick-2, Vidick-3, Aharonov-1, Aharonov-2, Aharonov-3, Dunjko, Oppenheim-1, Oppenheim-2, Oppenheim-3, Casini-1, Casini-2, Casini-3, Headrick-1, Headrick-2, Headrick-3, Fitzsimons

Broadcast on YouTube:  6/17(1) (2) (3)  6/18(1) (2)  6/19  6/20  6/21  6/22  6/24  6/25  6/26  6/27  6/28

Timetable of the 4th week (June 17 - 22)

Timetable of the 5th week (June 24 - 28)

[List of School Lecturers in It from Qubit School/Workshop, June 17-June 28, 2019]

• Dorit Aharonov (Hebrew University)  "Quantum Hamiltonian Complexity"

1) Quantum Hamiltonian Complexity 1 - Quantum NP hardness

The past two decades have seen remarkable developments in the study of the computational complexity of Hamiltonian related problem. Perhaps the single most important result for this development is Kitaev's insightful proof that the local Hamiltonian problem (the problem of estimating the ground energy of a given local Hamiltonian) is complete for the class QMA - the quantum analog of NP. I will explain the above notions and sketch Kitaev's beautiful proof. If time permits I will explain how the result was improved in the past couple of decades to more and more restricted families of Hamiltonians, providing deep insights into the hardness of finding the groundstate and ground energy of various classes of Hamiltonians.

2) Quantum Hamiltonian Complexity 2 - the evolving complexity map of Hamiltonians

Research in the past two decades has led to tremendous developments in our understanding of the computational complexity of Hamiltonians, branching out in different directions. We now have a pretty good understanding of which Hamiltonians are QMA-hard, which Hamiltonians can simulate each other, how and when we can use Hamiltonians for adiabatic and other types of computational university; and how all these problems are related to hardness of physical questions such as deciding whether a Hamiltonian is gapped or not in the thermodynamical limit. There are many more questions which are still open though... I will try to highlight the most important insights on our way towards completing the rich map of computational complexity of Hamiltonians.

3) Stoquastic Hamiltonians and derandomization/Joint work with Alex Grilo

Here we provide an unexpected link between quantum Hamiltonian complexity and a major open question in classical theoretical computer science: that of derandomization. We show that derandomization of the randomized analog of NP would follow from (and is in fact equivalent to) a certain quantum PCP like conjecture. More precisely, we show that if stoquastic (i.e. sign-problem-free) Hamiltonians can undergo a transformation which we call "gap amplification" (alternatively, PCP) then the randomized version of NP is in fact equal to NP. To do this, we show that the problem of deciding if the ground energy density of a given stoquastic Hamiltonian is 0 or above some constant gamma, is in NP; In a beautiful paper from 2008, Bravyi and Terhal showed that deciding the same question except with gamma being inverse polynomial, is complete for randomized NP. The proof involves notions like random walks, sign-problem free Hamiltonians, light cones, expansion and entanglement.

• Horacio Casini (Balseiro)  "Topics on entanglement and quantum field theory"

1- Basics of entanglement in quantum field theory
2- Entanglement and the renormalization group flow
3- Entanglement entropy and symmetries.


• Matthew Headrick (Brandeis)  "Holographic entanglement entropy"

Lecture 1: Basic introduction to holography and the Ryu-Takayanagi formula (for participants from outside the field)
Lecture 2: Holographic entanglement entropy in the time-dependent setting: the Hubeny-Rangamani-Takayanagi formula and its properties
Lecture 3: Bit threads: Basics and recent results

• Jonathan Oppenheim (University College London): Quantum Entanglement

Lecture 1) Quantum Resource Theories, and their application to thermodynamics and entanglement

Lecture 2) Quantum Shannon Theory (decoupling, quantum state merging, negative information, channels, mutual information vs coherent information, quantum Markov chains & recovery maps)

Lecture 3) Quantum Markovian dynamics, Classical stochastic processes, post-quantum dynamics (both in general, and the gravity theory in https://arxiv.org/abs/1811.03116)


• Thomas Vidick (Caltech)    "Topics in quantum complexity & cryptography"

This is a 3-lecture introduction to recent topics in quantum complexity theory. The first lecture will be mostly introductory and cover background in complexity theory, such as decision problems, quantum circuits, complexity classes, In the second lecture I will discuss the problem of (complexity-theoretic) verification: given a quantum device that contains a quantum state, or implements a certain computation, how can the state or computation be checked? In the third lecture I will present results from the area of self-testing, nonlocal games, and interactive proof systems, focusing on the role of entanglement.

• Beni Yoshida (Perimeter)  "Quantum Information Scrambling"   [References]

1. Operator growth and OTOC
2. Aspects of Haar randomness
3. Hayden-Preskill thought experiment


References for the lecture

• Verdran Dunjko (Leiden)  "Machine learning and Quantum Information Processing: the match and the hype" [Mini lecture]

The field of Quantum Machine Learning (QML) has been generating a substantial buzz in the last few years. QML research is typically driven by two basic objectives: finding ways in which quantum information processing (QIP) can help with machine learning (ML) problems, and, conversely, understanding the extent to which ML can be beneficially applied in QIP settings. In this overview talk, we will showcase how the parallels between the disciplines of QIP and ML which drive these main research lines of QML. We will present some of the latest developments both in the domains of quantum-applied and quantum-ehnanced machine learning, and discuss to what extent machine learning and QIP really are perfectly matched disciplines.

• Joseph Fitzsimons (Singapore)   "Secure and Verifiable Quantum Computation" [Mini lecture]

[List of Invited Speakers in IFQ workshop, June 17-June 28, 2019]

• Vijay Balasubramanian (UPenn)  "Quantum Complexity of Time Evolution with Chaotic Hamiltonians"

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e−iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion - the Eigenstate Complexity Hypothesis (ECH) - which bounds the overlap between off-diagonal energy eigenstate projectors and the k-local operators of the theory, and use it to show that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N=2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE \varsubsetneq BQP/poly and PSPACE \varsubsetneq BQSUBEXP/subexp, and the "fast-forwarding" of quantum Hamiltonians.

• Bartlomiej Czech (Tsinghua)  "What does the Chern-Simons formulation of AdS3 gravity tell us about complexity?"

I will explain how to realize the wavefunction of a CFT2 ground state as a network of Wilson lines in the Chern-Simons formulation of AdS3 gravity. The position and shape of the network encode the scale at which the wavefunction is defined. The structure of the network is that of a Matrix Product State (MPS) whose constituent tensors effect the Operator Product Expansion. A general argument suggests identifying the "density of complexity" of this MPS network with the extrinsic curvature of the bulk cutoff surface, which by the Gauss-Bonnet theorem agrees with the Complexity = Volume proposal.

• Jan de Boer (Amsterdam)  "Sewing entanglement wedges"
• Jens Eisert (Free University of Berlin)  "Holography and matchgate tensor networks"

The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks - which are briefly introduced in the talk - have come to provide toy models to understand such bulk-boundary correspondences, shedding light on connections between geometry and entanglement. In this talk, we we will introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1+1 dimensions [1]. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, and explain how critical data can be extracted. Within our framework, we also produce translation-invariant critical states by an efficiently contractible network dual to the multi-scale entanglement renormalization ansatz. Furthermore, we explore the correlation structure of states emerging in holographic quantum error correction. Using a machinery of holographic Majorana dimer models [2], we are able to compute boundary second moments for arbitrary states within the error correcting subspace. If time allows, we will hint at new connections to questions of complexity [3,4].

[1] Holography and criticality in matchgate tensor networks,
A. Jahn, M. Gluza, F. Pastawski, J. Eisert, Science Advances, in press (2019).
[2] Holographic Majorana dimer models of quantum error correction,
A. Jahn, M. Gluza, F. Pastawski, J. Eisert, arXiv:1905.03268 (2019).
[3] Circuit complexity, entangling power and the linear growth conjecture,
J. Eisert, in preparation (2019).
[4] Complexity and entanglement for thermofield double states,
S. Chapman, J. Eisert, L. Hackl, M. P. Heller, R. Jefferson, H. Marrochio, R. C Myers, SciPost Physics 6, 034 (2019).


• Daniel Harlow (MIT)  "Covariant Phase Space with Boundaries"
• Veronika Hubeny (UCDavis)  "Holographic Entropy Arrangement"

Linear combinations of entanglement entropies of subpartitions of a given quantum system ("information quantities") are conveniently described using a hyperplane arrangement in the entropy space. We will discuss such an arrangement for quantum states with holographic dual corresponding to a classical bulk geometry. This is greatly facilitated by working directly with HRT surfaces (rather than their areas), which can exhibit phase transitions. The intersection of allowed half-spaces corresponding to sign-definite information quantities constructs the "holographic entropy polyhedron" and is believed to delineate the holographic entropy cone, typically specified by extremal rays. We will summarize recent progress in the ongoing program to elucidate the structural properties of the arrangement and polyhedron, and discuss ensuing insights into holography. This talk will be contextualized by an earlier talk of Max Rota on the holographic marginal independence problem.

• Alexander Maloney (Mcgill)  "A Universal Formula for OPE Coefficients"
• Tomoyuki Morimae (YITP,Kyoto)  "Fine-grained quantum supremacy"

It is known that several sub-universal quantum computing models cannot be classically sampled in polynomial time unless the polynomial-time hierarchy collapses. All these results, however, do not exclude possibilities of exponential-time classical samplings. In this talk, we show that several sub-universal quantum computing models cannot be classically sampled even in certain exponential time under variants of some fine-grained complexity conjectures such as SETH, Orthogonal Vectors, and 3SUM. For details, see arXiv:1902.08382 and arXiv:1901.01637.

• Robert Myers (Perimeter)  "The First Law of Complexity"

We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the holographic complexity conjectures when the AdS vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state.

• Tatsuma Nishioka (Tokyo)  "Entanglement, free energy and C-theorem in DCFT"

The g-theorem is a prominent example of C-theorems in two-dimensional boundary CFT and the extensions are conjectured to hold in higher-dimensional BCFTs. On the other hand, much less is known for C-theorems in a CFT with conformal defects of higher codimensions. I will investigate the entanglement entropy across a sphere and sphere free energy as a candidate for a C-function in DCFT, and show they differ by a universal term proportional to the vev of the stress tensor. Based on this relation, I will propose to use the sphere free energy as a C-function in DCFT. This proposal unifies the previously known theorems and conjectures, and passes several checks, including a few examples in field theories and a holographic proof in simple gravity dual models of DCFTs.

• Yasunori Nomura (UC Berkeley)  "Spacetime and Universal Soft Modes -- Black Holes and Beyond"
• Hirosi Ooguri (Caltech/Kavli IPMU)  "Bounds on Mellin Amplitudes"
• Geoff Penington (Stanford)  "Entanglement Wedge Reconstruction and the Information Paradox"

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $\beta/2\pi \log S_{BH}$ into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall.

By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

• Xiao-liang Qi (Stanford)  "Operator size growth in the SYK model"
• Mark Van Raamsdonk (UBC)  "Black hole microstate cosmology"

We consider states of holographic CFTs defined by modifying the standard disk path integral that gives the vacuum state with the insertion of a boundary. We argue that these states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.

• Mukund Rangamani (UCDavis)  "Topological string entanglement"

I will describe how to understand entanglement entropy in topological string theory, using the open/closed topological string duality. Specifically, I will describe how the information about the replica construction of Chern-Simons theory can be uplifted directly onto the closed string and show that it provides a meaningful definition of reduced density matrices in topological string theory.

• Shinsei Ryu (Chicago)  "Entanglement negativity in many-body systems"

We will discuss entanglement negativity, a measure of quantum entanglement, in many-body quantum systems, in particular, those which appear in condensed matter physics, such as topologically ordered phases and conformal field theories.

• Subir Sachdev (Harvard)  "From SYK models to Planckian metals and charged black holes"

The SYK model describes fermions with all-to-all random interactions in a compressible phase without quasiparticle excitations. I will describe how this model, and its extensions, realize two distinct physical systems: (i) Planckian metals with a linear-in-temperature resistivity and a transport scattering time which is largely independent of the strength of interactions (ii) charged black holes at low temperatures with an AdS_2 horizon.

• Eva Silverstein (Stanford)  "Recent developments in de Sitter holography"

Both empirical observations and the mostly-positive potential energy of string theory demand a more complete framework for quantum gravity. This requires formulating finite bulk regions with a positive scalar potential energy. These regions fluctuate, but at large radius they admit a good semiclassical approximation, consistent with the possibility of a large-N strongly coupled holographic dual description. In this talk we develop such a dual formulation obtained from a combination of the $T\bar T$ trajectory applied to a holographic CFT, a universal generalization of it which incorporates a relevant deformation, and contributions to the trajectory dual to bulk matter field dynamics. This supplies a missing step in the dS/dS correspondence, which yields a concrete interpretation of the Gibbons-Hawking entropy as entanglement entropy between two isomorphic sectors in the dual theory. Independent calculations of the entanglement entropy for a half space matches between the two sides of the duality at the level of pure gravity. A similar trajectory provides a formulation of the de Sitter static patch. Finally, we investigate subregion dualities and connections to quantum error correction in this framework and outline numerous additional directions for further research.

• Wei Song (Tsinghua)  "Exploring toy models of the Kerr/CFT correspondence"
• Erik Tonni (SISSA)  "On entanglement hamiltonians in 1D free lattice models"

The reduced density matrix of a spatial subsystem can be written as the exponential of the entanglement hamiltonian, hence this operator contains a lot of information about the entanglement of the bipartition. In a harmonic chain and in a chain of free fermions, we present numerical studies concerning the temporal evolution of the entanglement hamiltonians and of the contours for the entanglement entropy of an interval after a global quench. For a free Dirac fermion on the line and in its ground state, we also discuss the derivation of the CFT expression for entanglement hamiltonian of an interval as the continuum limit of the corresponding lattice results.

• Sandip Trivedi (TIFR)  "Near-Extremal Black Holes and the JT Model"

TBA

• Herman Verlinde (Princeton)  "ER=EPR revisited: on the entropy of a wormhole"
• Frank Verstraete (Ghent/Vienna)  "Symmetries of Entanglement Hamiltonians: from TFT to CFT"
• Michael Walter (Amsterdam)  "Entanglement renormalization and conformal field theory"

The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories. Joint work with Freek Witteveen, Volkher Scholz, and Brian Swingle (arXiv:1905.08821).

[Oral Presentations in IFQ workshop, June 17-June 28, 2019]

• Pablo Bueno (Centro Atomico Bariloche)
  "New results on the entanglement entropy of singular regions in CFTs"

I will present new results involving the structure of divergences and universal terms of the entanglement and Renyi entropies for singular regions. I will start with a quick review of previous results in various dimensions. Then, I will argue that for (3+1)-dimensional free CFTs, entangling regions emanating from vertices give rise to a universal quadratically logarithmic contribution controlled by a local integral over the curve formed by the intersection of the entangling surface with a unit sphere centered at the vertex. While for circular and elliptic cones this term reproduces the general-CFT result, it vanishes for polyhedral corners. For those, I will argue that the universal contribution, which is logarithmic, is not controlled by a local integral, but rather it depends on details of the CFT in a complicated way, contrary to previous expectations. I will also refute a previous conjectural relation between the contribution coming from a wedge in (3+1) dimensions and the one corresponding to a corner region of the same opening angle in the (2+1) dimensions. Finally, I will show that the mutual information of two regions that touch at a point is not necessarily divergent, as long as the contact is through a sufficiently sharp corner and I will provide examples of singular entangling regions which do not modify the structure of divergences of the entanglement entropy compared with smooth surfaces.

Based on: arXiv:1904.11495, coauthored by Horacio Casini and William Witczak-Krempa

• Alex Buser (Caltech)
  "Quantum Algorithms for Lattice Gauge Theories"

What is the computational complexity of our universe? Does a universal quantum computer have sufficient power to efficiently simulate any process occurring in nature? A resolution of this question, known as the physical Church-Turing thesis, in either direction would have exciting implications for the future of theoretical physics. Building upon previous work on quantum simulation of scalar field theories, we discuss progress towards the efficient simulation of relativistic scattering processes in SU(3) Yang-Mills theory as a stepping stone towards the realization of the full standard model as a quantum simulation. Such an accomplishment would constitute significant progress towards resolving the physical Church-Turing thesis. We focus in particular on the efficient representation of the gauge field configuration space using qubits, the preparation of suitable initial scattering states, and the measurement of local observables.

• Joan Camps (University College London)
  "Superselection Sectors of Gravitational Subregions"

We study the division of the phase space of general relativity across subregions. Demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical---translates into a certain condition on the symplectic form. The gravitational subregions that satisfy this condition are bounded by surfaces of extremal area, and the 'centre variables' of their phase space are the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition discards local deformations of the entangling surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension 2.

• Pawel Caputa (YITP, Kyoto Univ.)
  "Quantum gravity and finite cut-off AdS"
• Shira Chapman (University of Amsterdam)
  "Holographic Complexity for Defects Distinguishes Action from Volume"

We explore the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect. We focus on a Randall-Sundrum type model of a thin AdS2 brane embedded in AdS3. We find that, using the "complexity=volume" proposal, the presence of the defect generates a logarithmic divergence in the complexity of the full boundary state with a coefficient which is related to the central charge and to the boundary entropy. For the "complexity=action" proposal we find that the complexity is not influenced by the presence of the defect. This is the first case in which the results of the two holographic proposals differ so dramatically. We consider also the complexity of the reduced density matrix for subregions enclosing the defect. We explore two bosonic field theory models which include two defects on opposite sides of a periodic domain. We point out that for a compact boson, current free field theory definitions of the complexity would have to be generalized to account for the effect of zero-modes.

• Zachary Kenneth Fisher (Perimeter)
  "Energy positivity and maximal volume susceptibility"

A beautiful and simple geometrical argument (published in 1807.02186) shows that maximal volume slices obey a strong superadditivity relation. We study second-order perturbations to the boundary conditions of maximal volume surfaces in asymptotically AdS spaces, and extract from the volume computation the off-diagonal terms in the variation. These off-diagonal terms, which we call the maximal volume susceptibility, must be positive by strong superadditivity. The positivity of this susceptibility gives new lower bounds for the expectation value of the timelike energy density in holographic CFTs.

• Damian A Galante (University of Amsterdam)
  "De Sitter horizons and holography"

We explore asymptotically AdS2 solutions of a particular two-dimensional dilaton-gravity theory. In the deep interior, these solutions flow to the cosmological horizon of dS2. We calculate various matter perturbations at the linearised and non-linear level. We consider both Euclidean and Lorentzian perturbations. The results can be used to characterise the features of a putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is assessed through the soft mode action at the AdS2 boundary, as well as the behaviour of shockwave type solutions.

• Yingfei Gu (Harvard University)
  "On the relation between the magnitude and exponent of OTOCs"
• Felix Haehl (UBC)
  "Effective field theory of large-c CFTs"

I will describe effective field theory methods to elucidate the physics of CFTs with a large number of degrees of freedom. I will focus on two-dimensional theories, but also comment on the one-dimensional case (related to the SYK model) and higher-dimensional generalizations. I will argue that the effective field theory of Goldstone modes of broken conformal symmetry provides a useful computational and conceptual framework. As a first application, we can compute 2k-point out-of-time-order correlators diagnosing quantum chaos. Another application involves a reformulation of ideas related to kinematic space and conformal blocks.

• Eliot Hijano (UBC)
  "Flat holography from AdS/CFT: From CFT correlators to scattering amplitudes"

The application of the holographic principle to geometries beyond AdS is expected to address many fundamental questions about quantum gravity. I will discuss recent developments in the context of flat holography, focusing on the map between CFT physics and flat space scattering processes.

• Nicholas Hunter-Jones (Perimeter Institute)
  "Models of complexity growth and random quantum circuits"
• Aitor Lewkowycz (Stanford University)
  "Maximal volumes and Euclidean variations"
• Henry Lin (Princeton University)
  "Symmetry Generators of Nearly AdS_2"

We explicitly construct three gauge invariant operators in both the SYK model and NAdS2 gravity, which correspond to the three Killing vectors of AdS2. Roughly speaking, these operators move particles in the interior while keeping the boundaries approximately fixed. We verify that in the Schwarzian limit, commutators of these operators satisfy an approximate SL(2) algebra. These operators govern the low energy SL(2) spectrum of the eternal traversable wormhole, and are closely related to chaos in the out of time order correlation functions.

• Javier Magan (Centro Atomico Bariloche)
  "Entanglement, superselection sectors and holography"

In this talk we describe an approach to analyze the universal terms of entanglement entropy in theories with local symmetries. These theories have a structure of superselection sectors which mirrors the structure of representations of the symmetry group. We review how this structure leaves a physical imprint in the vacuum sector of the theory, in particular through a violation of the so-called Haag duality. We then describe how this imprint affects the universal terms of entanglement entropy. Results will be given in the context of finite and Lie groups, systems with spontaneous symmetry breaking and excited states. Finally we describe how the approach apply to holographic scenarios, where the size of Haag duality violation is measured by minimal bulk areas.

• Dominik Neuenfeld (University of British Columbia)
  "Quantum information in scattering, IR divergences and asymptotic states"
• Tokiro Numasawa (McGIll University)
  "Late Time Quantum Chaos of Return Amplitude in the SYK model"

In this talk, we study the return amplitude, which is the overlap between the initial state and the time evolved state, in the Sachdev-Ye-Kitaev (SYK) model. Initial states are taken to be product states in a spin basis. We numerically study the return amplitude by exactly diagonalizing the Hamiltonian. We also derive the analytic expression for the return amplitude in random matrix theory. The SYK results match with the random matrix expectation. We also study the time evolution under the different Hamiltonian that describes the traversable wormholes in holographic context. The time evolution now depends on the choice of initial product states. The results are again explained by random matrix theory. In the symplectic ensemble cases, we observed an interesting pattern of the return amplitude where they show the second dip, ramp and plateau like behavior.

• Onkar Parrikar (University of Pennsylvania)
  "Soft modes from Black hole microstates"

We study the phase space of excitations around an incipient black hole in the half-BPS sector of N=4 Super Yang Mills theory, both from the AdS and CFT perspectives. On the gravity side, we identify a soft mode on the stretched horizon, which is absent in microstates. We explicitly construct and coarse-grain the phase space in the CFT, and explain the emergence of the soft mode from the microscopic degrees of freedom of the black hole.

• Charles Rabideau (Vrije Universiteit Brussel / University of Pennsylvania)
  "The dual of non-extremal area: differential entropy in higher dimensions"

The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-extremal surfaces that are not necessarily boundary-anchored. In general, the physics outside such surfaces is associated to observers restricted to a time-strip in the dual boundary field theory. When the latter is two-dimensional, it is known that the differential entropy associated to the strip computes the length of the dual bulk curve, and has an interpretation in terms of the information cost in Bell pairs of restoring correlations inaccessible to observers in the strip. A general realization of this formalism in higher dimensions is unknown. We first prove a no-go theorem eliminating candidate expressions for higher dimensional differential entropy based on entropic c-theorems. Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions. Our proposal stems from the physical requirement that differential entropy must be locally finite and conformally invariant. Demanding cancellation of the well-known UV divergences of entanglement entropy in field theory guides us to our conjecture, which we test for surfaces in AdS4. Our results suggest a candidate c-function for field theories in arbitrary dimensions.

• Massimiliano Rota (UCSB)
  "The holographic marginal independence problem"
• Gabor Sarosi (University of Pennsylvania)
  "Dual of the bulk symplectic form and the volume of maximal slices in AdS/CFT"

I will explain how to understand the symplectic structure of the gravitational phase space in AdS in terms of the quantum overlap in the holographically dual CFT. As an application, I will use this to study the boundary description of the volume of maximal Cauchy slices. I will construct the boundary deformation that is conjugate to the volume in empty AdS, and the thermofield double at infinite time. I will explain the bulk interpretation of this deformation and speculate on its boundary interpretation. This will motivate a concrete version of the complexity equals volume conjecture, where the boundary complexity is defined as the energy of geodesics in the Kahler geometry of path integral states.

• Bogdan Stoica (Brandeis)
  "Einstein Equation from p-adic Strings"
• Kotaro Tamaoka (YITP, Kyoto Univ.)
  "A Generalized Entanglement Entropy and Holography"

We generalize the entanglement entropy so that it can extract the minimal surfaces (Ryu-Takayanagi surfaces) anchored on not boundary but bulk. First, we explain properties of the generalized one and its basic ingredients. Then, we explicitly compute the generalized entropy for mixed states in two-dimensional CFT with the bulk dual. We will see agreement with the entanglement wedge cross section, a generalized version of the minimal surfaces. This talk is based on 1809.09109.

• Tomonori Ugajin (OIST)
  "Perturbative expansions of Renyi relative divergences and holography"

We develop a novel way to perturbatively calculate Rényi relative divergences and related quantities without using replica trick as well as analytic continuation. We explicitly determine the form of the perturbative term at any order by an integral along the modular flow of the unperturbed state. By applying the prescription to a class of reduced density matrices in conformal field theory, we find that the second order term of certain linear combination of the divergences has a holographic expression in terms of bulk symplectic form, which is a one parameter generalization of the statement ``Fisher information = Bulk canonical energy’’.

• Ying Zhao (IAS)
  "Operator size and symmetry"

[Poster Presenters on June 19]

Gong Show slides on June 19

[Poster Presenters on June 26]

Gong Show slides on June 26