Dynamical fields in de Sitter from CFT entanglement

Size: px
Start display at page:

Download "Dynamical fields in de Sitter from CFT entanglement"

Transcription

1 Dynamical fields in de Sitter from CFT entanglement Michał P. Heller Perimeter Institute for Theoretical Physics, Canada based on with J. de Boer, R. Myers and Yasha Neiman

2 Introduction

3 Differential entropy and hole-ography Balasubramanian, de Boer, Chowdhury, Czech & Heller Consider a CFT2 in the vacuum (say on S 1 of length of an interval of an angular opening 2 L ) and entanglement entropy S( ) = c 3 log(2l µ sin ) Consider now an infinite family of intervals given by ( ) and compute E = Z 2 0 d S 0 ( ( )) This novel UV-finite quantity is called differential entropy. In a holographic CFT2 it measures areas of closed curves on a constant-t slice of AdS3 1/11

4 Kinematic space Czech, Lamprou, McCandlish & Sully One can introduce a partial order on the set of intervals for which we calculate EE A A A B B B Timelike Spacelike Lightlike This (partially) motivates introducing the light-cone coordinates v = + and considering space with the volume form u =! v Sdu^dv and SSA turns out to v S 0. For the vacuum we obtain c! = 12 sin 2 du ^ dv ( ) The minimal metric compatible with this volume form and the partial order is ds 2 = c 12 sin 2 ( ) du dv = c 12 sin 2 ( ) 2/11 d 2 + d 2 de Sitter2!

5 Question behind this work Is there more to this Lorentzian structure than merely ordering intervals on a constant time slice of a CFT2? 3/11

6 Dynamics in de Sitter

7 Entanglement first law Consider small perturbations of some reference density matrix = 0 + The change in the entropy is equal to the change in the modular Hamiltonian S = tr ( log ) S 0 = hh mod i In general, H mod = log is unknown, but for reduced density matrices for spherical entangling surfaces in the CFTD vacuum it turns out to be fixed by conformality Z ~x 2< 2 H mod = c 0 2 d (D 1) x 2 ~x 2 2 T Casini, Huerta & Myers As a result, the change in the entanglement entropy for small perturbations of 0i is S = 2 Z ~x 2< 2 d (D 1) x 2 ~x 2 2 ht i 4/11

8 Entanglement first law yields dynamics in de Sitter In two dimensions (on a plane) we simply have S(, ) = 2 Z + dx 2 ( x) 2 2 ht i(x) at fixed ht i(x) S(, ) + x It is straightforward to check that 1 p a p gg b S 2 L 2 S =0 with g ab dx a dx b = L2 being the inflationary patch of de Sitter2! 2 d 2 + d 2 5/11

9 Specific example: universal excited state Any CFT has T µ operator, hence T ( 0, 0 ) 0i is an universal excitation in CFT2 s cf. Nozaki, Numasawa & Takayanagi ht i = h0 T ( 0 +, 0 ) T (,x) T ( 0, 0 ) 0i h0 T ( 0 +, 0 ) T ( 0, 0 ) 0i ( ) 4 Entanglement first law: S(, ) = 2 Z + dx 2 ( x) 2 2 ht i(x) ds2 analogue of the bulk-boundary smearing function by Kabat et al. 6/11

10 Generalization to higher spins in CFT2 The exploratory idea of Hijano & Kraus is the following: H mod = Z z2 z 1 (z z2 )(z z 1 ) dz T (z) + antiholomorphic z 2 z 1 H mod,3 = 3 Z z2 z 1 dz so in the presence of a higher spin current (here spin-3 current ) one can try 2 (z z2 )(z z 1 ) W (z) + antiholomorphic z 2 z 1 W Any quantity behaving as fields in de Sitter with Z + dx 2 ( x) 2 2 f(x) leads to a dynamical m 2 L 2 = 2 perturbation in entanglement entropy Hijano & Kraus construction m 2 L 2 = 2 m 2 L 2 = 6 7/11

11 Generalization to higher dimensions The first law for any CFT in D spacetime dimensions S = 2 Z ~x 2< 2 d (D 1) x 2 ~x 2 2 ht i implies propagation in D-dimensional de Sitter 1 p a p gg b S D L 2 S =0 with g ab dx a dx b = L2 being the inflationary patch of de SitterD. 2 ( d 2 + d~x 2 ) Note that free field theories have 1 many higher spin currents. see, e.g., Maldacena & Zhiboedov By extrapolating we might expect then 8/11 1 many fields in de SitterD

12 Relation to Einstein s equations in AdS In 2013 several groups were able to derive linearized Einstein s equations from the Ryu-Takayanagi proposal and the first law of entanglement entropy. In Takayanagi et al. showed that linearized Einstein s equations in AdS3 give Linear combination gives our wave equation on ds2: S A (,l,t)=0. 2 l/2 2 (l/2) 2 In Bhattacharya and Takayanagi obtained from Einstein s equations in AdS4 We see here that this equation in any D has nothing to do with a 2-derivative geometry and follows purely from the underlying conformal symmetry. 9/11

13 Summary and open problems

14 Summary ongoing work with Rob Myers and Guifre Vidal Entanglement in excited states organizes itself in a Lorentzian way: r a r a ds D S m 2 S =0 with m 2 L 2 ds D = D, e.g. for in T ( 0, 0) 0i ECFT2 and = L2. ds 2 ds 2 2 ( d 2 + d 2 ) This statement applies to any CFT in any D provided the first law holds! The statement concerns constant time slices in a CFT. For theories with higher spin charges: one dynamical field in dsd for each charge. 10/11

15 Some open problems Is recent explosion of emergent geometries an artifact of considering CFTs? Does auxiliary de Sitter = kinematic space? Higher dimensional generalization of differential entropy and hole-ography? Other fields in de Sitter, in particular gravitons? Nonlinear eoms? New holography? Local operators in de Sitter (generalization of Kabat et al.)? see Xiao Xiao Link with MERA / cmera? 11/11

Kinematic Space 2: Seeing into the bulk with Integral Geometry. Sam McCandlish. Stanford University

Kinematic Space 2: Seeing into the bulk with Integral Geometry. Sam McCandlish. Stanford University Kinematic Space 2: Seeing into the bulk with Integral Geometry Sam McCandlish Stanford University Work in progress with: Bartek Czech, Lampros Lamprou, Ben Mosk, James Sully 1 How do we probe the bulk?

More information

Dynamics of Entanglement Entropy From Einstein Equation

Dynamics 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 information

Tensor Networks, Renormalization and Holography (overview)

Tensor Networks, Renormalization and Holography (overview) KITP Conference Closing the entanglement gap: Quantum information, quantum matter, and quantum fields June 1 st -5 th 2015 Tensor Networks, Renormalization and Holography (overview) Guifre Vidal KITP Conference

More information

Local bulk physics from Intersecting Modular Hamiltonians

Local bulk physics from Intersecting Modular Hamiltonians Local bulk physics from Intersecting Modular Hamiltonians arxiv:1703.06523 D. Kabat and G. Lifschytz Crete regional meeting July 2017 Introduction How does bulk physics arise from the CFT? How do the degrees

More information

From Path Integral to Tensor Networks for AdS/CFT

From Path Integral to Tensor Networks for AdS/CFT Seminar @ Osaka U 2016/11/15 From Path Integral to Tensor Networks for AdS/CFT Kento Watanabe (Center for Gravitational Physics, YITP, Kyoto U) 1609.04645v2 [hep-th] w/ Tadashi Takayanagi (YITP + Kavli

More information

31st Jerusalem Winter School in Theoretical Physics: Problem Set 2

31st 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 information

Information Metric and Holography

Information 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 information

From Black holes to Qubits through String Theoretic Microscopes

From Black holes to Qubits through String Theoretic Microscopes ICHEP Formal Theory Development, July 10 th, 2018 @ Seoul From Black holes to Qubits through String Theoretic Microscopes Tadashi Takayanagi Yukawa Institute for Theoretical Physics Kyoto University 1

More information

Reconstructing Bulk from Boundary: clues and challenges

Reconstructing 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 information

Disentangling Topological Insulators by Tensor Networks

Disentangling 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 information

SPACETIME FROM ENTANGLEMENT - journal club notes -

SPACETIME 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 information

Holographic entanglement entropy beyond AdS/CFT

Holographic 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 information

Entanglement Inequalities

Entanglement 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 information

Gravity Actions from Tensor Networks

Gravity 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 information

arxiv: v2 [hep-th] 30 Mar 2018

arxiv: v2 [hep-th] 30 Mar 2018 Prepared for submission to JHEP Linearized Einstein s Equation around pure BTZ from Entanglement Thermodynamics arxiv:1803.06484v [hep-th] 30 Mar 018 Partha Paul, a,b Pratik Roy. c a Institute of Physics,

More information

Review 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 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 information

Holographic entanglement entropy

Holographic 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 information

21 Holographic Entanglement Entropy

21 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 information

Some applications of integral geometry in AdS/CFT

Some applications of integral geometry in AdS/CFT Some applications of integral geometry in AdS/CFT Xing Nov 2nd @ USTC Outline Review of integral geometry OPE block and reconstruction of bulk operators Entanglement renormalization Entanglement entropy

More information

Exact holography and entanglement entropy from one-point functions

Exact 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 information

arxiv: v2 [hep-th] 25 Dec 2017

arxiv: v2 [hep-th] 25 Dec 2017 Modular Berry Connection arxiv:1712.07123v2 [hep-th] 25 Dec 2017 Bart lomiej Czech, 1 Lampros Lamprou, 2 Samuel McCandlish, 3 and James Sully 4 1 Institute for Advanced Study, Princeton, NJ, USA 2 Massachusetts

More information

Entanglement Entropy in Flat Holography

Entanglement 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 information

Quantum Entanglement and the Geometry of Spacetime

Quantum 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 information

Quantum Information and Entanglement in Holographic Theories

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 information

10 Interlude: Preview of the AdS/CFT correspondence

10 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 information

AdS/CFT Correspondence and Entanglement Entropy

AdS/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 information

GEOMETRY AND ENTROPY James Sully

GEOMETRY AND ENTROPY James Sully GEOMETRY AND ENTROPY James Sully B.CZECH, X.DONG, JS arxiv:1406.4889 Motivation What does a theory of quantum gravity look like? Gravity is often described in different situations as: 1. A coarse-grained/effective

More information

A Holographic Description of Black Hole Singularities. Gary Horowitz UC Santa Barbara

A Holographic Description of Black Hole Singularities. Gary Horowitz UC Santa Barbara A Holographic Description of Black Hole Singularities Gary Horowitz UC Santa Barbara Global event horizons do not exist in quantum gravity: String theory predicts that quantum gravity is holographic:

More information

Emergent gravity. Diana Vaman. Physics Dept, U. Virginia. September 24, U Virginia, Charlottesville, VA

Emergent gravity. Diana Vaman. Physics Dept, U. Virginia. September 24, U Virginia, Charlottesville, VA Emergent gravity Diana Vaman Physics Dept, U. Virginia September 24, U Virginia, Charlottesville, VA What is gravity? Newton, 1686: Universal gravitational attraction law F = G M 1 M 2 R 2 12 Einstein,

More information

EPR Pairs, Local Projection and Quantum Teleportation in Holography

EPR Pairs, Local Projection and Quantum Teleportation in Holography Strings and Fields 2016, 2016/08/10 @ YITP, Kyoto EPR Pairs, Local Projection and Quantum Teleportation in Holography Kento Watanabe (YITP, Kyoto) arxiv: 1604.01772 [hep-th] (will appear in JHEP) with

More information

Universal entanglement of non-smooth surfaces

Universal 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 information

arxiv: v3 [hep-th] 11 Feb 2015

arxiv: 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 information

EPR Pairs, Local Projection and Quantum Teleportation in Holography

EPR 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 information

Holographic Entanglement Entropy

Holographic 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 information

Anomalies and Entanglement Entropy

Anomalies 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 information

Holographic Entanglement Entropy for Surface Operators and Defects

Holographic Entanglement Entropy for Surface Operators and Defects Holographic Entanglement Entropy for Surface Operators and Defects Michael Gutperle UCLA) UCSB, January 14th 016 Based on arxiv:1407.569, 1506.0005, 151.04953 with Simon Gentle and Chrysostomos Marasinou

More information

Causal Evolution of Bulk localized Excitations in AdS from CFT

Causal 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 information

Black Holes are Alpha-Bit Sup

Black 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 information

HIGHER SPIN DUALITY from THERMOFIELD DOUBLE QFT. AJ+Kenta Suzuki+Jung-Gi Yoon Workshop on Double Field Theory ITS, ETH Zurich, Jan 20-23,2016

HIGHER SPIN DUALITY from THERMOFIELD DOUBLE QFT. AJ+Kenta Suzuki+Jung-Gi Yoon Workshop on Double Field Theory ITS, ETH Zurich, Jan 20-23,2016 HIGHER SPIN DUALITY from THERMOFIELD DOUBLE QFT AJ+Kenta Suzuki+Jung-Gi Yoon Workshop on Double Field Theory ITS, ETH Zurich, Jan 20-23,2016 Overview } Construction of AdS HS Gravity from CFT } Simplest

More information

Bulk local states on the black holes in AdS/CFT

Bulk local states on the black holes in AdS/CFT Bulk local states on the black holes in AdS/CFT Kanato Goto The University of Tokyo,Komaba Holography,Quantum Entanglement and Higher Spin Gravity, Feb.6 th -7 th @YITP,Kyoto Based on the work in progress

More information

arxiv: v2 [hep-th] 13 Sep 2015

arxiv: 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 information

CFT PROBES OF BULK GEOMETRY

CFT 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 information

Holographic Geometries from Tensor Network States

Holographic Geometries from Tensor Network States Holographic Geometries from Tensor Network States J. Molina-Vilaplana 1 1 Universidad Politécnica de Cartagena Perspectives on Quantum Many-Body Entanglement, Mainz, Sep 2013 1 Introduction & Motivation

More information

It from Qubit Summer School

It from Qubit Summer School It from Qubit Summer School July 27 th, 2016 Tensor Networks Guifre Vidal NSERC Wednesday 27 th 9AM ecture Tensor Networks 2:30PM Problem session 5PM Focus ecture MARKUS HAURU MERA: a tensor network for

More information

Stress tensor correlators from holography

Stress tensor correlators from holography Stress tensor correlators from holography Aninda Sinha Indian Institute of Science, Bangalore 1 Mainly based on 1405.7862 with Kallol Sen. partly on 1401.5089 with Shamik Banerjee, Arpan Bhattacharyya,

More information

Theory of Quantum Matter: from Quantum Fields to Strings

Theory of Quantum Matter: from Quantum Fields to Strings Theory of Quantum Matter: from Quantum Fields to Strings Salam Distinguished Lectures The Abdus Salam International Center for Theoretical Physics Trieste, Italy January 27-30, 2014 Subir Sachdev Talk

More information

Quantum Null Energy Condition A remarkable inequality in physics

Quantum 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 information

Holography, thermalization and heavy-ion collisions I

Holography, thermalization and heavy-ion collisions I Holography, thermalization and heavy-ion collisions I Michał P. Heller Perimeter Institute for Theoretical Physics, Canada National Centre for Nuclear Research, Poland 1202.0981 [PRL 108 191601 (2012)]

More information

CAUSAL WEDGES in AdS/CFT

CAUSAL 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 information

A toy model for the Kerr/CFT. correspondence

A toy model for the Kerr/CFT. correspondence A toy model for the Kerr/CFT correspondence Monica Guică University of Pennsylvania with G. Compѐre, M.J. Rodriguez Motivation universal entropy for black holes good microscopic understanding only for

More information

Holographic Entanglement Entropy

Holographic 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 information

Quantum Operations in CFTs and Holography

Quantum 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 information

Quantum gravity and entanglement

Quantum 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 information

D.Blanco, H.C., L.Y.Hung, R. Myers (2013)

D.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 information

Entanglement entropy and the F theorem

Entanglement 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 information

Gauge / gravity duality in everyday life. Dan Kabat Lehman College / CUNY

Gauge / gravity duality in everyday life. Dan Kabat Lehman College / CUNY Gauge / gravity duality in everyday life Dan Kabat Lehman College / CUNY Queens College - 11/8/2017 Outline 1. About the title...* 2. What is it? 3. What is it good for? 4. My own interest: gauge => gravity

More information

Overview: Entanglement Entropy

Overview: 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 information

Holographic Entanglement and Interaction

Holographic Entanglement and Interaction Holographic Entanglement and Interaction Shigenori Seki RINS, Hanyang University and Institut des Hautes Études Scientifiques Intrication holographique et interaction à l IHES le 30 janvier 2014 1 Contents

More information

Holographic Entanglement Beyond Classical Gravity

Holographic 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 information

Holography for Black Hole Microstates

Holography 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 information

Duality and Holography

Duality and Holography Duality and Holography? Joseph Polchinski UC Davis, 5/16/11 Which of these interactions doesn t belong? a) Electromagnetism b) Weak nuclear c) Strong nuclear d) a) Electromagnetism b) Weak nuclear c) Strong

More information

A Proof of the Covariant Entropy Bound

A 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 information

BLACK HOLES IN 3D HIGHER SPIN GRAVITY. Gauge/Gravity Duality 2018, Würzburg

BLACK HOLES IN 3D HIGHER SPIN GRAVITY. Gauge/Gravity Duality 2018, Würzburg BLACK HOLES IN 3D HIGHER SPIN GRAVITY Gauge/Gravity Duality 2018, Würzburg What is a Black Hole? What is a Black Hole? In General Relativity (and its cousins): Singularity What is a Black Hole? In General

More information

Holographic Cosmology Beyond Inflation? Mark Trodden! University of Pennsylvania

Holographic Cosmology Beyond Inflation? Mark Trodden! University of Pennsylvania Holographic Cosmology Beyond Inflation? Mark Trodden! University of Pennsylvania Workshop: Status and Future of Inflationary Theory! University of Chicago, August 22-24, 2014 Questions Haven t been thinking

More information

Why we need quantum gravity and why we don t have it

Why we need quantum gravity and why we don t have it Why we need quantum gravity and why we don t have it Steve Carlip UC Davis Quantum Gravity: Physics and Philosophy IHES, Bures-sur-Yvette October 2017 The first appearance of quantum gravity Einstein 1916:

More information

Introduction to AdS/CFT

Introduction to AdS/CFT Introduction to AdS/CFT Who? From? Where? When? Nina Miekley University of Würzburg Young Scientists Workshop 2017 July 17, 2017 (Figure by Stan Brodsky) Intuitive motivation What is meant by holography?

More information

9 Symmetries of AdS 3

9 Symmetries of AdS 3 9 Symmetries of AdS 3 This section consists entirely of exercises. If you are not doing the exercises, then read through them anyway, since this material will be used later in the course. The main goal

More information

On the calculation of entanglement entropy in quantum field theory

On 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 information

Black Hole Formation in CFT

Black 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 information

HOLOGRAPHIC PROBES! COLLAPSING BLACK HOLES OF! Veronika Hubeny! Durham University & Institute for Advanced Study

HOLOGRAPHIC 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 information

Holographic renormalization and reconstruction of space-time. Kostas Skenderis Southampton Theory Astrophysics and Gravity research centre

Holographic renormalization and reconstruction of space-time. Kostas Skenderis Southampton Theory Astrophysics and Gravity research centre Holographic renormalization and reconstruction of space-time Southampton Theory Astrophysics and Gravity research centre STAG CH RESEARCH ER C TE CENTER Holographic Renormalization and Entanglement Paris,

More information

Entanglement, geometry and the Ryu Takayanagi formula

Entanglement, 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 information

Scale invariance on the lattice

Scale invariance on the lattice Coogee'16 Sydney Quantum Information Theory Workshop Feb 2 nd - 5 th, 2016 Scale invariance on the lattice Guifre Vidal Coogee'16 Sydney Quantum Information Theory Workshop Feb 2 nd - 5 th, 2016 Scale

More information

Entanglement and the Bekenstein-Hawking entropy

Entanglement 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 information

Perturbative Proof of the Covariant Entropy Bound

Perturbative 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 information

Gordon Research Conference Correlated Electron Systems Mount Holyoke, June 27, 2012

Gordon 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 information

Properties of entropy in holographic theories

Properties of entropy in holographic theories 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

More information

arxiv:hep-th/ v3 24 Apr 2007

arxiv:hep-th/ v3 24 Apr 2007 Anti-de Sitter boundary in Poincaré coordinates C. A. Ballón Bayona and Nelson R. F. Braga Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 Brazil Abstract

More information

Tensor network renormalization

Tensor network renormalization Walter Burke Institute for Theoretical Physics INAUGURAL CELEBRATION AND SYMPOSIUM Caltech, Feb 23-24, 2015 Tensor network renormalization Guifre Vidal Sherman Fairchild Prize Postdoctoral Fellow (2003-2005)

More information

5. a d*, Entanglement entropy and Beyond

5. 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 information

Time Evolution of Holographic Complexity

Time 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 information

Emergent Causality in Holography

Emergent 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 information

Aspects of Renormalized Entanglement Entropy

Aspects 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 information

Quantum Entanglement of locally perturbed thermal states

Quantum 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 information

Entanglement Holonomies

Entanglement Holonomies MIT-CTP/5029 Entanglement Holonomies arxiv:1807.04276v1 [hep-th] 11 Jul 2018 Bart lomiej Czech, a Lampros Lamprou, b Leonard Susskind c a Institute for Advanced Study, Princeton, NJ 08540, USA b Center

More information

Hyperscaling violation and entanglement entropy in gauge/string theory

Hyperscaling violation and entanglement entropy in gauge/string theory Hyperscaling violation and entanglement entropy in gauge/string theory K. Narayan Chennai Mathematical Institute Introduction, summary Lightcone SYM, string theory, AdS plane waves AdS plane waves, hyperscaling

More information

BOUNDING NEGATIVE ENERGY WITH QUANTUM INFORMATION, CAUSALITY AND A LITTLE BIT OF CHAOS

BOUNDING NEGATIVE ENERGY WITH QUANTUM INFORMATION, CAUSALITY AND A LITTLE BIT OF CHAOS BOUNDING NEGATIVE ENERGY WITH QUANTUM INFORMATION, CAUSALITY AND A LITTLE BIT OF CHAOS based on arxiv: 1706.09432 with: Srivatsan Balakrishnan, Zuhair Khandker, Huajia Wang Tom Faulkner University of Illinois

More information

Holographic relations at finite radius

Holographic relations at finite radius Mathematical Sciences and research centre, Southampton June 11, 2018 RESEAR ENT Introduction The original example of holography in string theory is the famous AdS/FT conjecture of Maldacena: - String theory

More information

Quantum mechanics and the geometry of space4me

Quantum mechanics and the geometry of space4me Quantum mechanics and the geometry of space4me 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 information

Symmetries, Horizons, and Black Hole Entropy. Steve Carlip U.C. Davis

Symmetries, Horizons, and Black Hole Entropy. Steve Carlip U.C. Davis Symmetries, Horizons, and Black Hole Entropy Steve Carlip U.C. Davis UC Davis June 2007 Black holes behave as thermodynamic objects T = κ 2πc S BH = A 4 G Quantum ( ) and gravitational (G) Does this thermodynamic

More information

Holography of compressible quantum states

Holography of compressible quantum states Holography of compressible quantum states New England String Meeting, Brown University, November 18, 2011 sachdev.physics.harvard.edu HARVARD Liza Huijse Max Metlitski Brian Swingle Compressible quantum

More information

Higher Spin AdS/CFT at One Loop

Higher 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 information

Thermalization after holographic bilocal quench

Thermalization after holographic bilocal quench Prepared for submission to JHEP Thermalization after holographic bilocal quench arxiv:1706.07390v3 [hep-th] 10 Oct 017 Irina Ya. Aref eva, Mikhail A. Khramtsov, Maria D. Tikhanovskaya Steklov Mathematical

More information

Holographic Entanglement Entropy. (with H. Casini, M. Huerta, J. Hung, M. Smolkin & A. Yale) (arxiv: , arxiv: )

Holographic 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 information

arxiv: v2 [hep-th] 4 Jul 2017

arxiv: v2 [hep-th] 4 Jul 2017 arxiv:1611.08581 Towards a ds/mera correspondence Raj Sinai Kunkolienkar and Kinjal Banerjee BITS, Pilani K. K. Birla Goa Campus Zuarinagar, Goa India (Dated: July 6, 2017) arxiv:1611.08581v2 [hep-th]

More information

Black Holes, Holography, and Quantum Information

Black Holes, Holography, and Quantum Information Black Holes, Holography, and Quantum Information Daniel Harlow Massachusetts Institute of Technology August 31, 2017 1 Black Holes Black holes are the most extreme objects we see in nature! Classically

More information

arxiv: v1 [hep-th] 4 May 2017

arxiv: 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 information

Three-dimensional gravity. Max Bañados Pontificia Universidad Católica de Chile

Three-dimensional gravity. Max Bañados Pontificia Universidad Católica de Chile Max Bañados Pontificia Universidad Católica de Chile The geometry of spacetime is determined by Einstein equations, R µ 1 2 Rg µ =8 G T µ Well, not quite. The geometry is known once the full curvature

More information

arxiv: v1 [hep-th] 20 May 2015

arxiv: v1 [hep-th] 20 May 2015 Prepared for submission to JHEP SU-ITP-15/7 Integral Geometry and Holography arxiv:155.5515v1 [hep-th] 2 May 215 Bartłomiej Czech a Lampros Lamprou a Samuel McCandlish a James Sully b a Stanford Institute

More information

Quantum Entanglement in Holography

Quantum Entanglement in Holography Quantum Entanglement in Holography Xi Dong Review talk Strings 2018, OIST, Okinawa, Japan June 27, 2018 Quantum entanglement Correlation between parts of the full system Simplest example: Ψ = Quantum entanglement

More information