Holographic Entanglement and Interaction
|
|
- Archibald Singleton
- 6 years ago
- Views:
Transcription
1 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
2 Contents 1. Quantum entanglement and holography [S. Ryu and T. Takayanagi, Phys.Rev.Lett. 96 (2006) ] 2. EPR = ER conjecture [J. Maldacena and L. Susskind, arxiv: ] 3. Accelerating quark and anti-quark [K. Jensen and A. Karch, Phys.Rev.Lett. 111 (2013) ] 4. Gluon scattering [SS and S.-J. Sin, to appear] 2
3 Quantum entanglement and holography 3
4 Quantum entanglement Let s consider two systems: A and B Hilbert space: H A H B { i A } { i B } basis A general state in total system is denoted by ψ tot = i,j c ij i A j B If If c ij = c A i c B j c ij = c A i c B j, it is a non-entangled state., it is an entangled state. What is an order parameter of entanglement? Entanglement Entropy 4
5 Density matrix: for Ψ H A H B Reduced density matrix ρ tot = ΨΨ ρ A := tr B ρ tot = j Bj ( ΨΨ ) j B The entanglement entropy is defined by Von Neumann entropy as S A := tr(ρ A log ρ A ) 5
6 EPR pair Einstein-Podolsky-Rosen pair [Einstein-Podolsky-Rosen, Phys.Rev. 47 (1935) 777] entangled two particles A B e.g. a spin-0 particle decays to two spin-1/2 particles. Separate them from each other at long distance A B Observe A The state of B is determined. A and B are still entangled. 6
7 e.g. Consider the state Ψ = 1 2 ( A B A B ) Since the reduced density matrix is ρ A = 1 2 ( A A + A A ) we obtain the entanglement entropy S A = tr(ρ A log ρ A ) = log 2 Note that the pure state ρ P = 1 2 ( A + A )( A + A ) has zero entanglement entropy S P = tr(ρ P log ρ P )=0 So the entanglement entropy works as an order parameter. 7
8 Holographic entanglement entropy AdS/CFT correspondence (Holography) Field theory on boundary Gravity theory in bulk Partition function Wilson loop Z CFT = e S grav W = e Area(γ) Entanglement entropy S A = 1 4G N Area(γ) A z AdS A z A γ A γ boundary minimal surface A [Ryu-Takayanagi, PRL 96 (2006) ] 8
9 EPR = ER conjecture 9
10 ER bridge [Maldacena-Susskind, arxiv: ] Consider the eternal AdS-Schwarzschild black hole. There are two boundaries and two CFTs. H L,R n L,R = E n n L,R n L Future interior This eternal BH is described by the entangle state, Ψ = n e βe n/2 n L n R We can interpret this state in two ways: 1. a single black hole in thermal equilibrium [Israel, Phys.Lett.A57 (1976) 107] Left boundary Left exterior Right exterior Right boundary n Past interior R Penrose diagram 2. two black holes in disconnected spaces with a common time [Maldacena, hep-th/ ] 10
11 1. a single black hole in thermal equilibrium Define a fictitious thermofield Hamiltonian, H tf = H R H L, u(i which generates boosts. u() Ψ = n e βe n/2 n L n R is an eigenvector of H tf with eigenvalue zero. U t = const 2. two black holes in disconnected spaces with a common time The time evolution is generated by H = H R + H L Ψ(t) = n e βe n/2 e 2iE nt n L n R The state Ψ describes the two black holes at a specific instant, t =0. Even though the two black holes exist in separate non-interacting worlds, their geometry is connected by an Einstein-Rosen bridge (a wormhole). [Einstein-Rosen, Phys.Rev. 48 (1935) 73] 11
12 EPR = ER conjecture From the example of eternal black hole, we studied Quantum mechanics entanglement geometric interpretation Gravity two systems connected by ER bridge By extending this concept, Maldacena and Susskind conjectured pairs of entangled particles separate at a long distance ER bridge BH BH 12
13 Further extension Even for an entangled pair of particles, in a quantum theory of gravity, there must be a Planckian bridge between them. ER bridge Black Black hole hole Hawking radiation. 13
14 Accelerating quark and anti-quark 14
15 The holographic surface of accelerating quark and anti-quark 0.1,23(0$4! 3(0$4! x 2 = t 2 + b 2 z 2 [Xiao, PLB 665 (2008) 173]! "#$%&!'#%()*!+#$,-#./!! The trajectories of quark and anti-quark are causally disconnected on the world-sheet. t x z The quark and anti-quark are entangled by the wormhole that the open string goes through. [Jensen-Karch, PRL 111 (2013) ] 15
16 The entanglement of quark and anti-quark (EPR pair) The interaction between quark and anti-quark ER bridge (wormhole) on world-sheet Do other interacting particles also have ER bridge on world-sheet? Fortunately, we know the minimal surface in AdS that describes a gluon-gluon scattering.
17 Gluon scattering 17
18 Minimal surface solution for gluon scattering AdS 5 (momentum space) [Alday-Maldacena, JHEP 0706 (2007) 064] ds 2 = R2 r 2 (η µνdy µ dy ν + dr 2 ) y µ =2πk µ The solution of Nambu-Goto action r =0 IR boundary condition y 0 = y 1 = y 2 = α 1+β 2 sinh u 1 sinh u 2 cosh u 1 cosh u 2 + β sinh u 1 sinh u 2, α sinh u 1 cosh u 2 cosh u 1 cosh u 2 + β sinh u 1 sinh u 2, α cosh u 1 sinh u 2 cosh u 1 cosh u 2 + β sinh u 1 sinh u 2, y 3 =0, α r =, cosh u 1 cosh u 2 + β sinh u 1 sinh u 2 Mandelstam variables: s(2π) 2 = t(2π) 2 = 8α2 (1 β) 2, 8α2 (1 + β) 2. 18
19 AdS 5 (momentum space) AdS 5 T-dual transformation: m y µ = R2 z 2 mn n x µ, (position space) z = R2 r ds 2 = R2 z 2 (η µνdx µ dx ν + dz 2 ) The Alday-Maldacena solution is mapped to x 0 = R2 1+β2 sinh u + sinh u, 2α x + := x 1 + x 2 2 = R2 2 2α [(1 + β)u +(1 β) cosh u + sinh u ], x := x 1 x 2 2 = R2 2 2α [(1 β)u + +(1+β)sinhu + cosh u ], x 3 =0, where u ± := u 1 ± u 2 z = R2 2α [(1 + β) cosh u + +(1 β) cosh u ]. For later convenience, we introduce X µ := α R 2 x µ (µ =0, +,, 3), Z := α z ( 1) R2 19
20 Causal structure on world-sheet The induced metric on world-sheet [SS-Sin, to appear] ds 2 ws = R 2 g ++ du g + du + du + g du 2 g ++ = 4(1 + β)2 sinh 2 u + + 4(1 + β 2 ) [(1 + β) cosh u + (1 β) cosh u ] 2 2[(1+β) cosh u + +(1 β) cosh u ] 2, g + = 2(1 β 2 )sinhu + sinh u [(1 + β) cosh u + +(1 β) cosh u ] 2, g = 4(1 β)2 sinh 2 u + 4(1 + β 2 ) [(1 + β) cosh u + (1 β) cosh u ] 2 2[(1+β) cosh u + +(1 β) cosh u ] 2. Horizons g ++ =0: (1 β) cosh u =(1+β) cosh u + +2 (1 + β) 2 sinh 2 u + +1+β 2 g =0: (1+β) cosh u + =(1 β) cosh u +2 (1 β) 2 sinh 2 u +1+β 2 20
21 0 β < 1 β =0 X ± (, + ) ˆX ± := 2 π arctan X ± [ 1, 1] Z = Z = β =1/ red: g =0, dashed red: g ++ =0, dotted blue: g ++ = g
22 β =1 Regge limit: s with t fixed. X 0 = 1 2 sinh u + sinh u, X + = 1 2 u, X = 1 2 sinh u + cosh u, X 3 =0, Z = cosh u While g ++ is positive definite, g is negative in cosh u + > 2. 22
23 EPR = ER = Interaction? The entanglement is given by a wormhole Incoming gluons: g 1 (t 1 ) = A L (t 1 ) A R (t 1 ) g 2 (t 1 ) = B L (t 1 ) B R (t 1 ) Outgoing gluons: g 3 (t 2 ) = A L (t 2 ) B R (t 2 ) 1.0 g 4 (t 2 ) = B L (t 2 ) A R (t 2 ) The entanglement is induced by gluonic interaction. 23
24 There are two ways to see entanglement. 1. Internal entanglement g 1 (t 1 ) = A L (t 1 ) A R (t 1 ) 1 0 The open string endpoints in each gluon are entangled by the open string going through the wormhole. This is in the same way as the entanglement of quark and anti-quark. 24
25 2. Entanglement of gluons There are two channels
26 How can we measure the entanglement of gluons? i ) (naively) log of scattering amplitude The scattering amplitude corresponds to the Wilson loop which is given by the area of minimal surface. λ A e Area, S log A = log 1+β 2 + (divergent part) 2π 1 β ii) the length between boundaries at the contacting points We consider + (β) =R +u+ u + du + g++ u =0, (β) =R where we introduced the cutoff, z ( ). +u u du g u+ =0 2 αz R 2 =(1+β) cosh u + +1 β =(1 β) cosh u +1+β 6 2αz ± (β) =R log R log 1 ± β + O z 6log 1 S + (β)+ (β) =R + (divergent part) 1 β2 Anyway, diverges at the Regge limit, and vanishes at. β =1 S β =0 26
27 EPR = ER = Interaction 27
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 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 informationQuantum 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 information17 Eternal Black Holes and Entanglement
17 Eternal Black Holes and Entanglement References: This section is based mostly on Maldacena hep-th/0106112; see also the relevant section of Harlow s review lectures, 1409.1231. An eternal black hole
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 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 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 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 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 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 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 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 informationThe Information Paradox
The Information Paradox Quantum Mechanics and Black Holes FokionFest 22 December 2017, Athens Kyriakos Papadodimas CERN 1 Space-Time and Quantum Gravity Space-time at short scales/scattering at E & 1019
More informationIntroduction 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 informationQuantum Mechanics and the Black Hole Horizon
1 Quantum Mechanics and the Black Hole Horizon Kyriakos Papadodimas CERN and University of Groningen 9th Aegean summer school: Einstein s theory of gravity and its modifications Space-time, gravity and
More informationThe Gauge/Gravity correspondence: linking General Relativity and Quantum Field theory
The Gauge/Gravity correspondence: linking General Relativity and Quantum Field theory Alfonso V. Ramallo Univ. Santiago IFIC, Valencia, April 11, 2014 Main result: a duality relating QFT and gravity Quantum
More informationFrom 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 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 informationStrings and Black Holes
Strings and Black Holes Erik Verlinde Institute for Theoretical Physics University of Amsterdam General Relativity R Rg GT µν µν = 8π µν Gravity = geometry Einstein: geometry => physics Strings: physics
More informationHolographic 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 informationNTU Physics Department Chih-Hung Wu 吳智弘
NTU Physics Department Chih-Hung Wu 吳智弘 I. Spacetime Locality and ER=EPR Conjecture II. Construction of the Counter-example III. Debate with Professor J. Maldacena J. Maldacena and L.Susskind, Cool horizon
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 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 informationHolographic vortex pair annihilation in superfluid turbulence
Holographic vortex pair annihilation in superfluid turbulence Vrije Universiteit Brussel and International Solvay Institutes Based mainly on arxiv:1412.8417 with: Yiqiang Du and Yu Tian(UCAS,CAS) Chao
More informationHadronic phenomenology from gauge/string duality
Hadronic phenomenology from gauge/string duality Modern Trends in Field Theory, Joã o Pessoa 09/2006 Nelson R. F. Braga, IF, UFRJ String Theory Strong Interactions Experimental observation ( 1960) of an
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 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 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 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 informationLattice study of quantum entanglement in SU(3) Yang-Mills theory at zero and finite temperatures
Lattice study of quantum entanglement in SU(3) Yang-Mills theory at zero and finite temperatures Yoshiyuki Nakagawa Graduate School of Science and Technology, Niigata University, Igarashi-2, Nishi-ku,
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 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 informationSeminar presented at the Workshop on Strongly Coupled QCD: The Confinement Problem Rio de Janeiro UERJ November 2011
and and Seminar presented at the Workshop on Strongly Coupled QCD: The Problem Rio de Janeiro UERJ 28-30 November 2011 Work done in collaboration with: N.R.F. Braga, H. L. Carrion, C. N. Ferreira, C. A.
More informationarxiv: v1 [hep-th] 6 Feb 2018
Black Holes and Complexity Classes arxiv:1802.02175v1 [hep-th] 6 Feb 2018 Leonard Susskind Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060,
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 informationEPR 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 informationProjection Measurement and Holography
Seminar@Osaka, April 10, 2017 Projection Measurement and Holography Tokiro Numasawa Osaka University Particle Physics Theory Based on JHEP08(2016)077 arxiv:1604.01772 [hep-th] Collaboration with N.Shiba(Harvard)
More informationEmergent 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 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 informationSpiky strings, light-like Wilson loops and a pp-wave anomaly
Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arxiv:080.039 A. Tseytlin, M.K. arxiv:0804.3438 R. Ishizeki, A. Tirziu, M.K. Summary Introduction
More informationHolographic 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 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 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 informationQuantum phase transitions in condensed matter
Quantum phase transitions in condensed matter The 8th Asian Winter School on Strings, Particles, and Cosmology, Puri, India January 11-18, 2014 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD
More informationarxiv: v2 [hep-th] 24 May 2015
Electric fields and quantum wormholes arxiv:1504.06336v [hep-th] 4 May 015 Dalit Engelhardt, 1,, Ben Freivogel,, 3, and Nabil Iqbal, 1 Department of Physics and Astronomy, University of California, Los
More informationFrom 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 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 informationThemodynamics at strong coupling from Holographic QCD
Themodynamics at strong coupling from Holographic QCD p. 1 Themodynamics at strong coupling from Holographic QCD Francesco Nitti APC, U. Paris VII Excited QCD Les Houches, February 23 2011 Work with E.
More informationQuantum Gravity. Juan Maldacena. Institute for Advanced Study
Quantum Gravity Juan Maldacena Institute for Advanced Study November 2015 General Relativity produced two stunning predictions: Black holes Expanding universe Your math is great, but your physics is dismal
More informationUnruh effect and Holography
nd Mini Workshop on String Theory @ KEK Unruh effect and Holography Shoichi Kawamoto (National Taiwan Normal University) with Feng-Li Lin(NTNU), Takayuki Hirayama(NCTS) and Pei-Wen Kao (Keio, Dept. of
More informationQuantum Gravity in 2+1 Dimensions I
Quantum Gravity in 2+1 Dimensions I Alex Maloney, McGill University Nordic Network Meeting, 12-09 A. M. & { S. Giombi, W. Song, A. Strominger, E. Witten, A. Wissanji, X. Yin} Empirical Evidence that Canada
More informationDurham E-Theses. Exploring Holographic Chaos and Complexity REYNOLDS, ALAN,PAUL
Durham E-Theses Exploring Holographic Chaos and Complexity REYNOLDS, ALAN,PAUL How to cite: REYNOLDS, ALAN,PAUL (2018) Exploring Holographic Chaos and Complexity, Durham theses, Durham University. Available
More informationConformal Blocks, Entanglement Entropy & Heavy States
Conformal Blocks, Entanglement Entropy & Heavy States Pinaki Banerjee The Institute of Mathematical Sciences, Chennai April 25, 2016 arxiv : 1601.06794 Higher-point conformal blocks & entanglement entropy
More informationBlack Hole Entropy and Thermodynamics of Space=me
Black Hole Entropy and Thermodynamics of Space=me Ted Jacobson University of Maryland 1 Sadi Carnot How does the maximum efficiency of steam engines depend on the working fluid? Carnot: given the temperatures
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 informationBlack hole thermodynamics
Black hole thermodynamics Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Spring workshop/kosmologietag, Bielefeld, May 2014 with R. McNees and J. Salzer: 1402.5127 Main
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 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 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 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 informationHolographic Wilsonian Renormalization Group
Holographic Wilsonian Renormalization Group JiYoung Kim May 0, 207 Abstract Strongly coupled systems are difficult to study because the perturbation of the systems does not work with strong couplings.
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 informationApplications of AdS/CFT correspondence to cold atom physics
Applications of AdS/CFT correspondence to cold atom physics Sergej Moroz in collaboration with Carlos Fuertes ITP, Heidelberg Outline Basics of AdS/CFT correspondence Schrödinger group and correlation
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 informationHIGHER 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 informationNon-Equilibrium Steady States Beyond Integrability
Non-Equilibrium Steady States Beyond Integrability Joe Bhaseen TSCM Group King s College London Beyond Integrability: The Mathematics and Physics of Integrability and its Breaking in Low-Dimensional Strongly
More informationGauge/String Duality and Quark Anti-Quark Potential
Gauge/String Duality and Quark Anti-Quark Potential Nelson R. F. Braga, Universidade Federal do Rio de Janeiro Summary Historical facts relating String theory to Strong interactions AdS/CFT, gauge string
More informationHawking radiation and universal horizons
LPT Orsay, France June 23, 2015 Florent Michel and Renaud Parentani. Black hole radiation in the presence of a universal horizon. In: Phys. Rev. D 91 (12 2015), p. 124049 Hawking radiation in Lorentz-invariant
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 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 informationThe Role of Black Holes in the AdS/CFT Correspondence
The Role of Black Holes in the AdS/CFT Correspondence Mario Flory 23.07.2013 Mario Flory BHs in AdS/CFT 1 / 30 GR and BHs Part I: General Relativity and Black Holes Einstein Field Equations Lightcones
More informationHolographic Space Time
Holographic Space Time Tom Banks (work with W.Fischler) April 1, 2015 The Key Points General Relativity as Hydrodynamics of the Area Law - Jacobson The Covariant Entropy/Holographic Principle - t Hooft,
More informationAn Entropy depending only on the Probability (or the Density Matrix)
An Entropy depending only on the Probability (or the Density Matrix) December, 2016 The Entropy and Superstatistics The Entropy and Superstatistics Boltzman-Gibbs (BG) statistics works perfectly well for
More informationThermalization 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 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 informationBOUNDING 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 informationGlueballs at finite temperature from AdS/QCD
Light-Cone 2009: Relativistic Hadronic and Particle Physics Instituto de Física Universidade Federal do Rio de Janeiro Glueballs at finite temperature from AdS/QCD Alex S. Miranda Work done in collaboration
More informationTowards a holographic formulation of cosmology
Towards a holographic formulation of cosmology Gonzalo Torroba Stanford University Topics in holography, supersymmetry and higher derivatives Mitchell Institute, Texas A&M, April 2013 During the last century,
More informationQuantum Entanglement, Strange metals, and black holes. Subir Sachdev, Harvard University
Quantum Entanglement, Strange metals, and black holes Subir Sachdev, Harvard University Quantum entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen
More informationEternal black holes in Anti-de-Sitter
NSF-ITP-01-59 hep-th/0106112 Eternal black holes in Anti-de-Sitter Juan Maldacena Jefferson Physical Laboratory Harvard University Cambridge, MA 02138, USA Institute for Advanced Study Princeton, NJ 08540
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 information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.821 String Theory Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.821 F2008 Lecture 03: The decoupling
More informationProbing spacetime with a holographic relation between spacetime and entanglement
Probing spacetime with a holographic relation between spacetime and entanglement Rasmus Jaksland Norwegian University for Science and Technology Abstract This paper introduces and examines the prospects
More informationDuality 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 informationQuark-gluon plasma from AdS/CFT Correspondence
Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence
More informationHolographic thermalization of 2D CFT
Holographic thermalization of 2D CFT Shu Lin ( 林树 ) Sun Yat-Sen University ICTS, USTC, 9/8/2016 SL, Shuryak, PRD 2008 SL, PRD 2016 Outline Phenomenon of thermalization in physics Holographic description
More informationClassical AdS String Dynamics. In collaboration with Ines Aniceto, Kewang Jin
Classical AdS String Dynamics In collaboration with Ines Aniceto, Kewang Jin Outline The polygon problem Classical string solutions: spiky strings Spikes as sinh-gordon solitons AdS string ti as a σ-model
More informationThree-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 informationNonlocal Effects in Quantum Gravity
Nonlocal Effects in Quantum Gravity Suvrat Raju International Centre for Theoretical Sciences 29th Meeting of the IAGRG IIT Guwahati 20 May 2017 Collaborators Based on work with 1 Kyriakos Papadodimas
More informationCovariant Prescription of Holographic Entanglement Entropy in AdS 3 and BTZ Black Hole
Master Thesis Covariant Prescription of Holographic Entanglement Entropy in AdS 3 and BTZ Black Hole Mario Benites High Energy Physics, Department of Theoretical Physics, School of Engineering Sciences
More informationViscosity Correlators in Improved Holographic QCD
Bielefeld University October 18, 2012 based on K. Kajantie, M.K., M. Vepsäläinen, A. Vuorinen, arxiv:1104.5352[hep-ph]. K. Kajantie, M.K., A. Vuorinen, to be published. 1 Motivation 2 Improved Holographics
More informationGauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg
Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity
More informationRadiation from the non-extremal fuzzball
adiation from the non-extremal fuzzball Borun D. Chowdhury The Ohio State University The Great Lakes Strings Conference 2008 work in collaboration with Samir D. Mathur (arxiv:0711.4817) Plan Describe non-extremal
More informationM5-branes and Wilson Surfaces! in AdS7/CFT6 Correspondence
M5-branes and Wilson Surfaces! in AdS7/CFT6 Correspondence Hironori Mori (Osaka Univ.) based on arxiv:1404.0930 with Satoshi Yamaguchi (Osaka Univ.) 014/05/8, Holographic vistas on Gravity and Strings
More informationAdS/CFT and Second Order Viscous Hydrodynamics
AdS/CFT and Second Order Viscous Hydrodynamics Micha l P. Heller Institute of Physics Jagiellonian University, Cracow Cracow School of Theoretical Physics XLVII Course Zakopane, 20.06.2007 Based on [hep-th/0703243]
More informationLight-Front Holography and Gauge/Gravity Correspondence: Applications to Hadronic Physics
Light-Front Holography and Gauge/Gravity Correspondence: Applications to Hadronic Physics Guy F. de Téramond University of Costa Rica In Collaboration with Stan Brodsky 4 th International Sakharov Conference
More informationAutocorrelators in models with Lifshitz scaling
Autocorrelators in models with Lifshitz scaling Lárus Thorlacius based on V. Keränen & L.T.: Class. Quantum Grav. 29 (202) 94009 arxiv:50.nnnn (to appear...) International workshop on holography and condensed
More informationLinear Confinement from AdS/QCD. Andreas Karch, University of Washington work with Ami Katz, Dam Son, and Misha Stephanov.
Linear Confinement from AdS/QCD Andreas Karch, University of Washington work with Ami Katz, Dam Son, and Misha Stephanov. Excited Rho Mesons 6 (from PARTICLE DATA BOOK) Experiment 0.933 n 5 m 2 n, GeV
More informationYun Soo Myung Inje University
On the Lifshitz black holes Yun Soo Myung Inje University in collaboration with T. Moon Contents 1. Introduction. Transition between Lifshitz black holes and other configurations 3. Quasinormal modes and
More informationBlack holes, Holography and Thermodynamics of Gauge Theories
Black holes, Holography and Thermodynamics of Gauge Theories N. Tetradis University of Athens Duality between a five-dimensional AdS-Schwarzschild geometry and a four-dimensional thermalized, strongly
More information