Properties of entropy in holographic theories
|
|
- Thomas Sutton
- 5 years ago
- Views:
Transcription
1 Properties of entropy in holographic theories Matthew Headrick randeis University Contents 0 Definitions 1 Properties of entropy Entanglement entropy in QFT 3 Ryu-Takayanagi formula 6 Monogamy 8 5 SS of covariant holographic EE? 10 1
2 0 Definitions Suppose we have a quantum system in a state ρ (could be pure or mixed) Let,,... be disjoint subsystems (H = H H ) = etc. Reduced density matrix: ρ = tr c ρ Entanglement entropy: S() = tr ρ ln ρ Three examples ( is first bit): 1. ρ = 1 ( ) ( ). ρ = 1 ( ) 3. ρ = 1 ( ) = 1 ( ) ( ) 1 ( ) ( ) In all three cases, ρ = 1 ( ), S() = ln So entanglement entropy can be due to: (1) entanglement; () classical correlation; (3) being in a mixed state without entanglement or correlation; or a combination thereof 1 Properties of entropy ased purely on properties of Hilbert spaces & density matrices; no other physics input
3 One subsystem: S() 0, S() = 0 iff ρ is pure Hence S is a measure of mixedness Two subsystems: (1) raki-lieb: S() S() S() In particular if ρ is pure then S() = S() () Subadditivity: S() S() + S(), S() = S() + S() iff ρ = ρ ρ Hence mutual information I( : ) = S() + S() S() is a measure of correlation (classical + quantum) between,. In examples above: 1. ρ = 1 ( ) ( ) I( : ) = ln. ρ = 1 ( ) I( : ) = ln 3. ρ = 1 ( ) = 1 ( ) ( ) 1 ( ) ( ) I( : ) = 0 Mutual information is a key quantity in classical & quantum information theory. Numerous operational senses in which it measures total amount of correlation. Examples: I( : ) = S() S( ) = how much your ignorance about decreases if you know state of, where S( ) = S() S() = conditional entropy of given (N.. in quantum setting S( ) can be negative, so interpretation is less clear) I( : ) gives the rate at which information can reliably be sent over a noisy channel (Shannon) ound on correlators between normalized operators: (Wolf, Verstraete, Hastings, Cirac 07): ( O O O O ) I( : ) 3
4 Three subsystems: If mutual information measures total amount of correlation, then it should increase under adjoining another subsystem to or : I( : C) I( : ) i.e. S() + S(C) S(C) + S() Strong subadditivity. Easy to show at classical level; conjectured in quantum systems by Lanford, Robinson 68, proved by Lieb, Ruskai 73 Four subsystems: Constrained inequality (Linden, Winter 0): If I( : C) = I( : ) = I( : C), I( : CD) = I( : D) then I(C : D) I(C : ) Five or more subsystems: Infinite hierarchy of constrained inequalities (Cadney, Linden, Winter 11) Entanglement entropy in QFT In a QFT, we can take subsystems to be spatial regions:
5 In vacuum, or any low-energy state, EE is UV-divergent along boundary of, S() = ɛ D area( ) + (with subleading divergences in D ) or, in two dimensions, S() = c UV 6 ln ɛ #( ) + (Note that a generic state will have S() = ɛ 1 D vol(), so this is very little entanglement: ground states and low-energy states are special in that they are highly unentangled. This provides a massive simplification e.g. in simulations of lattice systems.) Mutual information is divergent along common boundary, I( : ) = ɛ D area( ) + rea-law divergence manifestly obeys SS, since area ( (C)) = area( ) + area( C) area( ) C lso obeys Linden-Winter constrained inequality, since if I( : C) = I( : ), I( : CD) = I( : D) 5
6 then C is separated from,, hence I(C : ) = 0, hence I(C : D) I(C : ) If, are separated then I( : ) is finite & universal. However, it is very difficult to compute in practice. E.g. for free compact scalar in 1 + 1, mutual information between two intervals is not known (Calabrese, Cardy, Tonni 09, 10) 3 Ryu-Takayanagi formula Ryu-Takayanagi formula for EE of a spatial region in a holographic theory dual to classical Einstein gravity ( large N, strong coupling ) in a state described in the bulk by a static, classical field configuration ( distinguished constant-time surfaces): S() = 1 ( ) min area(m) G N m where area(m) is computed w.r.t. spatial, Einstein-frame metric m means bulk region r s.t. r = m call minimizer m(), r() r() m() bulk Notes: 6 black hole m() = horizon
7 Is r() the holographic dual (in some sense) of ρ? Raamsdonk 1) (See also Czech, Karczmarek, Nogueira, Van Corrections believed to take general form (α = classical higher-derivative; G N = quantum = 1/N ): S() = 1 ( ) min area(m) + O(α ) + O(G 0 G N) N m See Hung, Myers, Smolkin 10, de oer, Kulaxizi, Parnachev 10 Ryu-Takayanagi formula obeys all the general properties listed above. Obviously S() 0. Triangle inequality is triangle inequality: m() m() m() Strong subadditivity (MH, Takayanagi 07): C S() + S(C) = m() m(c) = m(c) m() = S(C) + S() General, formal proof: Take r() = r() r(c), r(c) = r() r(c) Notes: 7
8 Proof is far simpler than proof of SS in quantum mechanics. General relativity knows some sophisticated quantum information theory! This proof (along with other tests of RT formula) automatically still holds in presence of higher-derivative (α ) corrections, but not quantum (G N ) corrections We will discuss Linden-Winter etc. below Monogamy We saw that mutual information is monotonic: (adjoining a system cannot decrease correlations). I( : C) I( : ) ut what do we expect for I( : C) vs. I( : ) + I( : C)? How are correlations correlated with each other? In principle three possibilities: 1. correlations are uncorrelated: I( : C) = I( : ) + I( : C). correlations are shared: I( : C) < I( : ) + I( : C) 3. correlations are distributed: I( : C) > I( : ) + I( : C) ll three behaviors are possible in general. Example of shared correlations: ρ C = 1 ( ) I( : C) = I( : ) = I( : C) = ln Example of distributed correlations: ρ C = 1 ( ) I( : C) = ln, I( : ) = I( : C) = 0. Define tripartite information : I 3 ( : : C) = I( : ) + I( : C) I( : C) = S() + S() + S(C) S() S(C) S(C) + S(C) 8
9 What happens in QFTs? rea-law divergence in QFT has I 3 = 0; reflects purely pairwise correlations across entangling surfaces C In gapped + 1 theories (for simply connected), S() = ɛ 1 area( ) γ In states with topological order, γ > 0, topological entanglement entropy (Kitaev & Preskill, Levin & Wen 05). Hence I 3 ( : : C) = γ < 0: correlations are distributed non-locally Free examples (Casini, Huerta 08): Massive fermion or boson: I 3 can be positive or negative depending on,, C Fermion in massless limit: I 3 0 for all,, C oson in massless limit: I 3 + for all,, C; after tracing over complement of C, longwavelength modes lead to shared correlations In holographic theories, RT formula implies I 3 ( : : C) 0 for any,, C (Hayden, MH, Maloney 11). Proof is more complicated version of holographic SS proof Inequalities of the form f( : C) f( : ) + f( : C), where f is a measure of entanglement, are called monogamy relations, because they reflect the fact that entanglement is never shared. In general, mutual information does not obey this inequality because it measures classical correlations in addition to entanglement Holds in presence of higher-curvature corrections, not quantum corrections 9
10 Implies Linden-Winter and Cadney-Linden-Winter inequalities. RT formula obeys every known applicable property of entropy Interpretation is not clear, but it suggests that correlations are distribute non-locally, as in topological order. May also suggest that correlations are dominantly in the form of entanglement 5 SS of covariant holographic EE? RT formula applies only to static bulk spacetimes, and region lying in constant-time slice Conjecture for covariant generalization by Hubeny, Rangamani, Takayanagi 07: replace minimal surface with minimal extremal surface. Has been applied to various systems, but subjected to fewer tests than static RT formula Two key changes compared to static case: Surface m() is co-dimension two in bulk spacetime; region r() is co-dimension one m() is not minimum but only extremum of area For both reasons, holographic proof of SS does not go through anymore: C S() + S(C) = m() m(c) = m(c) m() = S(C) + S() Question: does covariant HEE formula obey SS? 10
11 Tests (Callan, He, MH 1; see also llais, Tonni 11, Caceres, Kundu, Pedraza, Tangarife 13) We consider planar ds 3, TZ, ds 3 -Vaidya (preserve spatial translation symmetry) Regions,, C are adjacent single intervals (so, C, C are also single intervals). Two possibilities: constant-time: C non-constant-time: Constant-time intervals: Translation invariance: S() = s(l ), S() = s(l + l ), etc S() + S(C) S() + S(C) s (l) 0 S() + S(C) S(C) + S() s (l) 0 ds 3 : ) s(l) = c 3 ln ( l ɛ TZ: s(l) = c ( ) 1 3 ln sinh(πt L) πt ɛ
12 Vaidya (intervals at different times after the injection of energy): TZ 5 horizon ds shell x 1 UV thermalizes first, so short intervals show TZ behavior while long intervals show ds behavior Negative-energy Vaidya: x Transition from TZ to ds behavior leads to loss of concavity. Violation of SS is correlated with violations of null energy condition and second law (area theorem) Non-constant-time intervals: ds, TZ: S() = 1 (s( x + t) + s( x t)) Since s(l) obeys SS, S obeys SS Vaidya: SS was tested for many configurations. Trapezoid with, C null provides most stringent test, since SS saturated in ds, TZ 1
13 SS violated precisely when NEC violated ppearance of NEC is not surprising; known to be required for area theorem ousso covariant entropy bound holographic c-theorems... Proof? local proof for -dimensional theories can be obtained using geodesic deviation equation. Two assumptions required: Null energy condition bsence of conjugate points along geodesic (plausible but not proven for minimal geodesic) Does not cover cases where minimal surface jumps (phase transitions) Wall 1: Global proof; however, does not apply to spacetimes containing horizons complete proof would Provide a crucial check on HRT formula e an important new theorem in GR, at the level of the area theorem for black holes, and deepen our still-sketchy understanding of the entropy-area connection in GR 13
Quantum Information and Entanglement in Holographic Theories
Quantum Information and Entanglement in Holographic Theories Matthew Headrick randeis University Contents 1 asic notions 2 1.1 Entanglement entropy & mutual information............................ 2 1.2
More informationOverview: Entanglement Entropy
Overview: Entanglement Entropy Matthew Headrick Brandeis University January 27, 2014 Quantum Fields beyond Perturbation Theory KITP 0 Intro & disclaimer Over past 10 years, explosion of activity in entanglement
More informationQuantum Entanglement and the Geometry of Spacetime
Quantum Entanglement and the Geometry of Spacetime Matthew Headrick Brandeis University UMass-Boston Physics Colloquium October 26, 2017 It from Qubit Simons Foundation Entropy and area Bekenstein-Hawking
More informationBit Threads and Holographic Entanglement
it Threads and Holographic Entanglement Matthew Headrick randeis University Strings 2016, eijing ased on arxiv:1604.00354 [hep-th], with Michael Freedman Contents 1 How should one think about the minimal
More informationEntanglement, geometry and the Ryu Takayanagi formula
Entanglement, geometry and the Ryu Takayanagi formula Juan Maldacena Kyoto, 2013 Aitor Lewkowycz Lewkowycz, JM ArXiv:1304.4926 & Faulkner, Lewkowycz, JM, to appear Tom Faulkner Previously argued by Fursaev
More informationHolographic Entanglement Entropy. (with H. Casini, M. Huerta, J. Hung, M. Smolkin & A. Yale) (arxiv: , arxiv: )
v Holographic Entanglement Entropy (with H. Casini, M. Huerta, J. Hung, M. Smolkin & A. Yale) (arxiv:1102.0440, arxiv:1110.1084) Entanglement Entropy what is entanglement entropy? general tool; divide
More informationHolographic Entanglement Entropy
Holographic Entanglement Entropy Aninda Sinha Indian Institute of Science, Bangalore 1 1 DERIVATIONS of Holographic Entanglement Entropy Aninda Sinha Indian Institute of Science, Bangalore 1 1 Disclaimers!
More information21 Holographic Entanglement Entropy
21 Holographic Entanglement Entropy 21.1 The formula We now turn to entanglement entropy in CFTs with a semiclassical holographic dual. That is, we assume the CFT has a large number of degrees of freedom
More informationHolographic Entanglement Entropy
Motivation Time-dependent Multi-region Summary Holographic entanglement entropy for time dependent states and disconnected regions Durham University INT08: From Strings to Things, April 3, 2008 VH, M.
More informationBit Threads and Holographic Entanglement
it Threads and Holographic Entanglement Matthew Headrick randeis Uniersity ased on arxi:60400354 [hep-th], with Michael Freedman Entropy and area In semiclassical graity, entropies are related to surface
More informationEntanglement Entropy for Disjoint Intervals in AdS/CFT
Entanglement Entropy for Disjoint Intervals in AdS/CFT Thomas Faulkner Institute for Advanced Study based on arxiv:1303.7221 (see also T.Hartman arxiv:1303.6955) Entanglement Entropy : Definitions Vacuum
More informationHolographic Entanglement Beyond Classical Gravity
Holographic Entanglement Beyond Classical Gravity Xi Dong Stanford University August 2, 2013 Based on arxiv:1306.4682 with Taylor Barrella, Sean Hartnoll, and Victoria Martin See also [Faulkner (1303.7221)]
More informationReview of Holographic (and other) computations of Entanglement Entropy, and its role in gravity
Review of Holographic (and other) computations of Entanglement Entropy, and its role in gravity Entanglement Entropy what is entanglement entropy? general tool; divide quantum system into two parts and
More informationarxiv: v2 [hep-th] 13 Sep 2015
Non-linear Holographic Entanglement Entropy Inequalities for Single Boundary D CFT Emory Brown, 1, Ning Bao, 1, and Sepehr Nezami 3 1 Institute for Quantum Information and Matter Walter Burke Institute
More information31st Jerusalem Winter School in Theoretical Physics: Problem Set 2
31st Jerusalem Winter School in Theoretical Physics: Problem Set Contents Frank Verstraete: Quantum Information and Quantum Matter : 3 : Solution to Problem 9 7 Daniel Harlow: Black Holes and Quantum Information
More informationCAUSAL WEDGES in AdS/CFT
CUSL WEDGES in ds/cft Veronika Hubeny Durham University Gauge/Gravity Duality 2013 Max Planck Institute for Physics, 29 July 2013 to 2 ugust 2013 Based on: VH & M.Rangamani: 1204.1698, VH, M.Rangamani,
More informationEntanglement Entropy and AdS/CFT
Entanglement Entropy and AdS/CFT Christian Ecker 2 nd DK Colloquium January 19, 2015 The main messages of this talk Entanglement entropy is a measure for entanglement in quantum systems. (Other measures
More informationHolographic entanglement entropy beyond AdS/CFT
Holographic entanglement entropy beyond AdS/CFT Edgar Shaghoulian Kavli Institute for the Physics and Mathematics of the Universe April 8, 014 Dionysios Anninos, Joshua Samani, and ES hep-th:1309.579 Contents
More informationHolographic entanglement entropy
Holographic entanglement entropy Mohsen Alishahiha School of physics, Institute for Research in Fundamental Sciences (IPM) 21th Spring Physics Conference, 1393 1 Plan of the talk Entanglement entropy Holography
More informationAdS/CFT Correspondence and Entanglement Entropy
AdS/CFT Correspondence and Entanglement Entropy Tadashi Takayanagi (Kyoto U.) Based on hep-th/0603001 [Phys.Rev.Lett.96(2006)181602] hep-th/0605073 [JHEP 0608(2006)045] with Shinsei Ryu (KITP) hep-th/0608213
More informationSPACETIME FROM ENTANGLEMENT - journal club notes -
SPACETIME FROM ENTANGLEMENT - journal club notes - Chris Heinrich 1 Outline 1. Introduction Big picture: Want a quantum theory of gravity Best understanding of quantum gravity so far arises through AdS/CFT
More informationHolographic Entanglement of Purification
20 Years Later: The Many Faces of ds/cft @ Princeton, Oct.31-Nov.3, 2017 Holograhic ntanglement of Purification Tadashi Takayanagi Yukawa Institute for Theoretical Physics (YITP, Kyoto Univ. ased on arxiv:1708.09393
More informationarxiv: v1 [hep-th] 23 Dec 2013
Prepared for submission to JHEP RX-TH673 arxiv:1312.6717v1 [hep-th] 23 Dec 2013 General properties of holographic entanglement entropy Matthew Headrick Martin Fisher School of Physics, randeis University,
More informationCFT PROBES OF BULK GEOMETRY
CFT PROBES OF BULK GEOMETRY Veronika Hubeny Durham University May 24, 2012 Based on: VH: 1203.1044 VH & M.Rangamani: 1204.1698 OUTLINE Motivation & Background Features of Extremal Surfaces Probing Horizons
More informationBit Threads & Holographic Monogamy
Bit Threads & Holographic Monogamy Matthew Headrick Brandeis University Entanglement in Quantum Systems GGI Florence, June 2018 Based on arxiv:1604.00354 [hep-th] with M. Freedman & forthcoming work with
More informationD.Blanco, H.C., L.Y.Hung, R. Myers (2013)
D.Blanco, H.C., L.Y.Hung, R. Myers (2013) Renormalization group flow in the space of QFT Change in the physics with scale through the change of coupling constants with the RG flow. At fixed points there
More informationHolographic Entanglement entropy and second law of Black holes. Sudipta Sarkar
Holographic Entanglement entropy and second law of Black holes Sudipta Sarkar Indian Institute of Technology Gandhinagar Based on: arxiv:1504.04706, arxiv:1306.1623 In collaboration with Aron Wall (IAS),
More information재규격화군흐름, 녹채 & Holography 과홀로그래피
RG Flows, Entanglement 재규격화군흐름, 녹채 & Holography 과홀로그래피 Strings 2013 Sogang Univesity, Seoul Korea, 26-29 June 2013 New Dialogues in Theoretical Physics: Particle Physics Statistical Mechanics Renormalization
More informationEntanglement Inequalities
Entanglement Inequalities Hirosi Ooguri Walter Burke Institute for Theoretical Physics, Caltech Kavli IPMU, University of Tokyo Nafplion, Greece, 5 11 July 2015 1/44 Which CFT's have Gravity Duals? Which
More informationA Proof of the Covariant Entropy Bound
A Proof of the Covariant Entropy Bound Joint work with H. Casini, Z. Fisher, and J. Maldacena, arxiv:1404.5635 and 1406.4545 Raphael Bousso Berkeley Center for Theoretical Physics University of California,
More informationReconstructing Bulk from Boundary: clues and challenges
Reconstructing Bulk from Boundary: clues and challenges Ben Freivogel GRAPPA and ITFA Universiteit van Amsterdam Ben Freivogel () Reconstructing Bulk from Boundary May 24, 2013 1 / 28 Need quantum gravity
More informationDon Marolf 7/17/14 UCSB
Don Marolf 7/17/14 UCSB D=4: F = GM 2 /r 2, dimensionless coupling GE 2 /ħc 5 grows with E. Quantum fluctuations are a problem, growing at short distances. Growth must(?) stop somewhere (non trivial fixed
More informationAn Inverse Mass Expansion for Entanglement Entropy. Free Massive Scalar Field Theory
in Free Massive Scalar Field Theory NCSR Demokritos National Technical University of Athens based on arxiv:1711.02618 [hep-th] in collaboration with Dimitris Katsinis March 28 2018 Entanglement and Entanglement
More informationEntanglement entropy and the F theorem
Entanglement entropy and the F theorem Mathematical Sciences and research centre, Southampton June 9, 2016 H RESEARH ENT Introduction This talk will be about: 1. Entanglement entropy 2. The F theorem for
More informationAnomalies and Entanglement Entropy
Anomalies and Entanglement Entropy Tatsuma Nishioka (University of Tokyo) based on a work with A. Yarom (Technion) (to appear) T. Nishioka (Tokyo) Sep 10, 2015 @ Tohoku 1 / 35 Roles of entanglement entropy
More informationBit Threads and Holographic Monogamy
Bit Threads and Holographic Monogamy Shawn X. Cui, 1 Patrick Hayden, 1 Temple He, 2 Matthew Headrick, 3,4 Bogdan Stoica, 3,5 and Michael Walter 6 1 Stanford Institute for Theoretical Physics, Stanford
More informationGravity Actions from Tensor Networks
Gravity Actions from Tensor Networks [hep-th/1609.04645] with T. Takayanagi and K. Watanabe and ongoing work with P. Caputa, N. Kundu, T. Takayanagi, K. Watanabe Masamichi Miyaji Yukawa Institute for Theoretical
More informationEntanglement in Quantum Field Theory
Entanglement in Quantum Field Theory John Cardy University of Oxford DAMTP, December 2013 Outline Quantum entanglement in general and its quantification Path integral approach Entanglement entropy in 1+1-dimensional
More informationHolographic c-theorems and higher derivative gravity
Holographic c-theorems and higher derivative gravity James Liu University of Michigan 1 May 2011, W. Sabra and Z. Zhao, arxiv:1012.3382 Great Lakes Strings 2011 The Zamolodchikov c-theorem In two dimensions,
More informationOn the calculation of entanglement entropy in quantum field theory
On the calculation of entanglement entropy in quantum field theory Nakwoo Kim Physics Department Kyung Hee University July 5, 2017 RQIN 2017, YITP Kyoto Nakwoo Kim ( Physics Department Kyung Hee University
More informationBlack Holes are Alpha-Bit Sup
Black Holes are Alpha-Bit Sup arxiv:1706.09434, arxiv:1805.????? Patrick Hayden and Geoffrey Penington, Stanford University Preview Qubits are composite resources Another resource (that you have never
More informationAspects of Renormalized Entanglement Entropy
Aspects of Renormalized Entanglement Entropy Tatsuma Nishioka (U. Tokyo) based on 1207.3360 with Klebanov, Pufu and Safdi 1401.6764 1508.00979 with Banerjee and Nakaguchi T. Nishioka (Tokyo) Oct 15, 2015
More informationEntanglement & C-theorems
Entanglement & C-theorems Robert Myers Perimeter Institute (with Sinha; Casini, Huerta & Yale) spukhafte Fernwirkung = spooky action at a distance Quantum Entanglement different subsystems are correlated
More informationEntanglement entropy in a holographic model of the Kondo effect
Entanglement entropy in a holographic model of the Kondo effect Mario Flory Max-Planck-Institut für Physik University of Oxford 05.05.2015 Mario Flory Entanglement entropy & Kondo 1 / 30 Overview Part
More informationEntanglement Entropy in Flat Holography
Entanglement Entropy in Flat Holography Based on work with Qiang Wen, Jianfei Xu( THU), and Hongliang Jiang( The HKUST) East Asian Joint Workshop KEK Theory workshop 2017 Bekenstein Bardeen-Carter-Hawking
More informationQuantum Null Energy Condition A remarkable inequality in physics
Quantum Null Energy Condition A remarkable inequality in physics Daniel Grumiller Institute for Theoretical Physics TU Wien Erwin-Schrödinger Institute, May 2018 1710.09837 Equalities in mathematics and
More informationUniversal terms in the Entanglement Entropy of Scale Invariant 2+1 Dimensional Quantum Field Theories
Universal terms in the Entanglement Entropy of Scale Invariant 2+1 Dimensional Quantum Field Theories Eduardo Fradkin Department of Physics and Institute for Condensed Matter Theory, University of Illinois
More informationDisentangling Topological Insulators by Tensor Networks
Disentangling Topological Insulators by Tensor Networks Shinsei Ryu Univ. of Illinois, Urbana-Champaign Collaborators: Ali Mollabashi (IPM Tehran) Masahiro Nozaki (Kyoto) Tadashi Takayanagi (Kyoto) Xueda
More informationIntroduction to the Ryu-Takayanagi Formula
Introduction to the Ryu-Takayanagi Formula PHYS 48300 String Theory-1, Masaya Fukami {13 March 2018} 1 Introduction The idea of holography has played central roles in recent developments of string theory.
More informationHOLOGRAPHIC PROBES! COLLAPSING BLACK HOLES OF! Veronika Hubeny! Durham University & Institute for Advanced Study
HOLOGRAPHIC PROBES! OF! COLLAPSING BLACK HOLES Veronika Hubeny! Durham University & Institute for Advanced Study New frontiers in dynamical gravity workshop Cambridge, March 26, 2014 Based on work w/ H.
More information5. a d*, Entanglement entropy and Beyond
Motivation: role of higher curvature interactions on AdS/CFT calculations Overview: 1. Introductory remarks on c-theorem and CFT s 2. Holographic c-theorem I: Einstein gravity 3. Holographic c-theorem
More informationQuantum entanglement, it s entropy, and why we calculate it
Quantum entanglement, it s entropy, and why we calculate it Piotr Witkowski Max Planck Institute for Physics 14.7 2016 Munich 1 What is entanglement? 2 Quantifying entanglement the entropy 3 The (very)
More informationInformation Metric and Holography
11 th Vienna Central European Seminar Quantum and Gravity @ Univ. of Vienna, Nov.7-8, 015 Information Metric and Holography Tadashi Takayanagi Yukawa Institute for Theoretical Physics (YITP), Kyoto University
More informationEntanglement Entropy In Gauge Theories. Sandip Trivedi Tata Institute of Fundamental Research, Mumbai, India.
Entanglement Entropy In Gauge Theories Sandip Trivedi Tata Institute of Fundamental Research, Mumbai, India. On The Entanglement Entropy For Gauge Theories, arxiv: 1501.2593 Sudip Ghosh, Ronak Soni and
More informationExact holography and entanglement entropy from one-point functions
Exact holography and entanglement entropy from one-point functions O-Kab Kwon (Sungkyunkwan University) In collaboration with Dongmin Jang, Yoonbai Kim, Driba Tolla arxiv:1612.05066, 1610.01490 1605.00849
More informationGordon Research Conference Correlated Electron Systems Mount Holyoke, June 27, 2012
Entanglement, holography, and strange metals Gordon Research Conference Correlated Electron Systems Mount Holyoke, June 27, 2012 Lecture at the 100th anniversary Solvay conference, Theory of the Quantum
More informationEntanglement entropy and gauge fields
Entanglement entropy and gauge fields H. C., M.Huerta and A. Rosabal (2012) H. C., M. Huerta (2014) H. C., M. Huerta, in preparation Puzzling results Lattice calculations with extended lattice (Buividovich-Polikarpov,
More informationDynamics of Entanglement Entropy From Einstein Equation
YITP Workshop on Quantum Information Physics@YITP Dynamics of Entanglement Entropy From Einstein Equation Tokiro Numasawa Kyoto University, Yukawa Institute for Theoretical Physics based on arxiv:1304.7100
More informationUniversal entanglement of non-smooth surfaces
Universal entanglement of non-smooth surfaces Pablo Bueno IFT, Madrid Based on P.B., R. C. Myers and W. Witczak-Krempa, PRL 115, 021602 (2015); P.B. and R. C. Myers arxiv:1505.07842; + work in progress
More informationRG Flows, Entanglement & Holography Workshop. Michigan Center for Theore0cal Physics September 17 21, 2012
RG Flows, Entanglement & Holography Workshop Michigan Center for Theore0cal Physics September 17 21, 2012 Intersec0ons in Theore0cal Physics: Par$cle Physics Sta$s$cal Mechanics Renormalization Group Flows
More informationTime Evolution of Holographic Complexity
Time Evolution of Holographic Complexity Sotaro Sugishita (Osaka Univ.) based on arxiv:1709.10184 [JHEP 1711, 188 (2017)] with Dean Carmi, Shira Chapman, Hugo Marrochio, Robert Myers RIKEN-Osaka-OIST Joint
More informationarxiv: v2 [hep-th] 21 Dec 2014
arxiv:1412.3514v2 [hep-th] 21 Dec 2014 Inviolable energy conditions from entanglement inequalities Nima Lashkari, Charles Rabideau, Philippe Sabella-Garnier, Mark Van Raamsdonk Department of Physics and
More informationSecond law of black-hole thermodynamics in Lovelock theories of gravity
Second law of black-hole thermodynamics in Lovelock theories of gravity Nilay Kundu YITP, Kyoto Reference : 62.04024 ( JHEP 706 (207) 090 ) With : Sayantani Bhattacharyya, Felix Haehl, R. Loganayagam,
More informationarxiv: v1 [hep-th] 4 May 2017
Butterfly velocity and bulk causal structure arxiv:1705.01728v1 [hep-th] 4 May 2017 Xiao-Liang Qi 1, Zhao Yang 1 1 Department of Physics, Stanford University, Stanford, CA 94305, USA Abstract The butterfly
More informationBlack Hole Formation in CFT
Black Hole Formation in CFT Tom Hartman Cornell University 20 Years Later: The Many Faces of AdS/CFT PCTS November 2017 = Leinweber 2003 SS 1. How does gravity emerge? 2. In what theories? 3. Locality
More informationPerturbative Proof of the Covariant Entropy Bound
Perturbative Proof of the Covariant Entropy Bound Work in progress, with H. Casini, Z. Fisher, and J. Maldacena Raphael Bousso Berkeley Center for Theoretical Physics University of California, Berkeley
More informationEntanglement Entropy in 2+1 Chern-Simons Theory
Entanglement Entropy in 2+1 Chern-Simons Theory Shiying Dong UIUC With: Eduardo Fradkin, Rob Leigh, Sean Nowling arxiv: hep-th/0802.3231 4/27/2008 Great Lakes String Conference @ University of Wisconsin-Madison
More informationBlack Hole Entropy and Gauge/Gravity Duality
Tatsuma Nishioka (Kyoto,IPMU) based on PRD 77:064005,2008 with T. Azeyanagi and T. Takayanagi JHEP 0904:019,2009 with T. Hartman, K. Murata and A. Strominger JHEP 0905:077,2009 with G. Compere and K. Murata
More information20 Entanglement Entropy and the Renormalization Group
20 Entanglement Entropy and the Renormalization Group Entanglement entropy is very di cult to actually calculate in QFT. There are only a few cases where it can be done. So what is it good for? One answer
More informationArea Laws in Quantum Systems: Mutual Information and Correlations
ESI The Erwin Schrödinger International Boltzmanngasse 9 Institute for Mathematical Physics A-1090 Wien, Austria Area Laws in Quantum Systems: Mutual Information and Correlations Michael M. Wolf Frank
More informationQuantum Entanglement of locally perturbed thermal states
Quantum Entanglement of locally perturbed thermal states Joan Simón University of Edinburgh and Maxwell Institute of Mathematical Sciences Holography, strings and higher spins Swansea, March 20, 2015 Based
More informationOne-loop Partition Function in AdS 3 /CFT 2
One-loop Partition Function in AdS 3 /CFT 2 Bin Chen R ITP-PKU 1st East Asia Joint Workshop on Fields and Strings, May 28-30, 2016, USTC, Hefei Based on the work with Jie-qiang Wu, arxiv:1509.02062 Outline
More informationLinear response of entanglement entropy from holography
Linear response of entanglement entropy from holography Juan F. Pedraza June 7, 2017 Based on: arxiv:1602.05934, Sandipan Kundu & JFP arxiv:1705.10324, Sagar Lokhande, Gerben Oling & JFP Juan F. Pedraza
More informationQuantum mechanics and the geometry of spacetime
Quantum mechanics and the geometry of spacetime Juan Maldacena PPCM Conference May 2014 Outline Brief review of the gauge/gravity duality Role of strong coupling in the emergence of the interior Role of
More information10 Interlude: Preview of the AdS/CFT correspondence
10 Interlude: Preview of the AdS/CFT correspondence The rest of this course is, roughly speaking, on the AdS/CFT correspondence, also known as holography or gauge/gravity duality or various permutations
More informationHigher Spin AdS/CFT at One Loop
Higher Spin AdS/CFT at One Loop Simone Giombi Higher Spin Theories Workshop Penn State U., Aug. 28 2015 Based mainly on: SG, I. Klebanov, arxiv: 1308.2337 SG, I. Klebanov, B. Safdi, arxiv: 1401.0825 SG,
More informationRényi Entropy in AdS 3 /CFT 2 (with W symmetry)
EE HEE CFT Torus Conclusion Extras Bin Chen R Peking University International Conference on String Field Theory and Related Aspects May 11-15, 2015, CTP, Sichuan University, Chengdu EE HEE CFT Torus Conclusion
More informationHolographic Entanglement Entropy, Fractional Quantum Hall Effect and Lifshitz-like Fixed Point
Journal of Physics: Conference Series OPEN ACCESS Holographic Entanglement Entropy, Fractional Quantum Hall Effect and Lifshitz-like Fixed Point To cite this article: Tadashi Takayanagi 2013 J. Phys.:
More informationarxiv: v3 [hep-th] 11 Feb 2015
Entanglement density and gravitational thermodynamics DCPT-14/77, YITP-104, IPMU14-0359 arxiv:141.547v3 [hep-th] 11 Feb 015 Jyotirmoy Bhattacharya, 1, Veronika E. Hubeny, 1, Mukund Rangamani, 1,, 3, and
More informationOn a holographic quantum quench with a finite size effect
On a holographic quantum quench with a finite size effect Tomonori Ugajin (U. Tokyo KITP) Based on work in progress with G.Mandal, R.Sinha Holographic Vistas on gravity and strings YITP, 2014 Introduction
More informationComplexity and Spacetime
Complexity and Spacetime 1612.05439, 1706.03788 + to appear, with Alan Reynolds Simon Ross Centre for Particle Theory, Durham University 13 September 2017 Simon Ross (Durham) Complexity and Spacetime McGill
More informationarxiv: v2 [hep-th] 27 Jun 2013
MIT-CTP 4475 ntanglement Tsunami: Universal Scaling in Holographic Thermalization Hong Liu and S. Josephine Suh Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 0139
More informationEntanglement and the Bekenstein-Hawking entropy
Entanglement and the Bekenstein-Hawking entropy Eugenio Bianchi relativity.phys.lsu.edu/ilqgs International Loop Quantum Gravity Seminar Black hole entropy Bekenstein-Hawking 1974 Process: matter falling
More information19 Entanglement Entropy in Quantum Field Theory
19 Entanglement Entropy in Quantum Field Theory So far we have discussed entanglement in ordinary quantum mechanics, where the Hilbert space of a finite region is finite dimensional. Now we will discuss
More informationEPR Pairs, Local Projection and Quantum Teleportation in Holography
YITP long term workshop 2016, One Day Conference, 2016/06/08 @ YITP, Kyoto EPR Pairs, Local Projection and Quantum Teleportation in Holography Kento Watanabe (YITP, Kyoto) arxiv: 1604.01772 [hep-th] with
More informationRenormalized entanglement entropy and the number of degrees of freedom
Renormalize entanglement entropy an the number of egrees of freeom Hong Liu MIT Base on arxiv:1202.2070 with Mark Mezei Goal For any renormalizable quantum fiel theory, construct an observable which coul:
More informationCondensed Matter Physics in the City London, June 20, 2012
Entanglement, holography, and the quantum phases of matter Condensed Matter Physics in the City London, June 20, 2012 Lecture at the 100th anniversary Solvay conference, Theory of the Quantum World arxiv:1203.4565
More informationOne Loop Tests of Higher Spin AdS/CFT
One Loop Tests of Higher Spin AdS/CFT Simone Giombi UNC-Chapel Hill, Jan. 30 2014 Based on 1308.2337 with I. Klebanov and 1401.0825 with I. Klebanov and B. Safdi Massless higher spins Consistent interactions
More informationEntanglement, holography, and strange metals
Entanglement, holography, and strange metals University of Cologne, June 8, 2012 Subir Sachdev Lecture at the 100th anniversary Solvay conference, Theory of the Quantum World, chair D.J. Gross. arxiv:1203.4565
More informationCausal Evolution of Bulk localized Excitations in AdS from CFT
Causal Evolution of Bulk localized Excitations in AdS from CFT Kanato Goto The University of Tokyo, Komaba Particle Theory Group based on arxiv:1605.02835 KG and M.Miyaji and T.Takayanagi Kanato Goto (Tokyo
More informationQuantum Operations in CFTs and Holography
Strings2016 @ Beijing, Tsinghua, 2016, ug.1-5 Quantum Operations in CFTs and Holography Tadashi Takayanagi ( 高柳匡 ) Yukawa Institute for Theoretical Physics (YITP), Kyoto University Based on arxiv:1604.01772
More informationSymmetry protected entanglement between gravity and matter
Symmetry protected entanglement between gravity and matter Nikola Paunković SQIG Security and Quantum Information Group, IT Departamento de Matemática, IST in collaboration with Marko Vojinović GPF Group
More informationHolography and (Lorentzian) black holes
Holography and (Lorentzian) black holes Simon Ross Centre for Particle Theory The State of the Universe, Cambridge, January 2012 Simon Ross (Durham) Holography and black holes Cambridge 7 January 2012
More informationGerardo Adesso. Davide Girolami. Alessio Serafini. University of Nottingham. University of Nottingham. University College London
Gerardo Adesso University of Nottingham Davide Girolami University of Nottingham Alessio Serafini University College London arxiv:1203.5116; Phys. Rev. Lett. (in press) A family of useful additive entropies
More informationHolography for Black Hole Microstates
1 / 24 Holography for Black Hole Microstates Stefano Giusto University of Padua Theoretical Frontiers in Black Holes and Cosmology, IIP, Natal, June 2015 2 / 24 Based on: 1110.2781, 1306.1745, 1311.5536,
More informationDynamical fields in de Sitter from CFT entanglement
Dynamical fields in de Sitter from CFT entanglement Michał P. Heller Perimeter Institute for Theoretical Physics, Canada based on 1509.00113 with J. de Boer, R. Myers and Yasha Neiman Introduction Differential
More informationQuantum gravity and entanglement
Quantum gravity and entanglement Ashoke Sen Harish-Chandra Research Institute, Allahabad, India HRI, February 2011 PLAN 1. Entanglement in quantum gravity 2. Entanglement from quantum gravity I shall use
More informationEmergent Causality in Holography
Emergent Causality in Holography Netta Engelhardt Princeton University 20.6.18 Based mostly on: NE, Horowitz 16; NE 16; NE, Fischetti 17 Spacetime Emergence Holography: the equivalence of a higher-dim
More informationTowards a 2nd Law for Lovelock Theory
Towards a 2nd Law for Lovelock Theory Nilay Kundu YITP, Kyoto University This talk is based on the following preprint arxiv:1612.04024 [hep-th] Towards a second law for Lovelock theories Sayantani Bhattacharyya,
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More information