Quantum Entanglement and the Geometry of Spacetime
|
|
- Joanna Gibbs
- 6 years ago
- Views:
Transcription
1 Quantum Entanglement and the Geometry of Spacetime Matthew Headrick Brandeis University UMass-Boston Physics Colloquium October 26, 2017 It from Qubit Simons Foundation
2 Entropy and area Bekenstein-Hawking 74: kb c3 area(horizon) area(horizon) S= = kb 2 4GN ~ 4lP GN gravity Planck length ( cm) ~ quantum mechanics kb statistical mechanics What are the atoms of the black hole? Why is S area?
3 Entropy and area In any number d of dimensions, G N ~ has units of area ( L d 1 ) Natural unit in quantum gravity is Planck area Generalizations of Bekenstein-Hawking: De Sitter spacetime (Gibbons-Hawking 77): Holographic entropy bounds (Bekenstein 81, Bousso 99): for arbitrary closed surface in arbitrary spacetime How general is the area-entropy relation? What is its origin? clue: Holographic entanglement entropy (Ryu-Takayanagi 06) Vast but also limited generalization of Bekenstein-Hawking S = area(horizon) 4G N ~ To understand it, we first need to extend our notion of entropy S apple area 4G N ~ Jacobson 94 used area-entropy relation to derive Einstein equation
4 Entanglement Entropy Classical mechanics: definite state certain outcome for any measurement Quantum mechanics: definite state uncertain outcomes for some measurements Example: "i measurement of S z definitely gives ~ measurement of S x gives ~ 1 or with equal probability 2 ~ When only certain kinds of measurements are allowed, a definite (pure) state will effectively be indefinite (mixed) Suppose a system has two parts, but we can only measure one part Spin singlet state: Bi = p 1 ( "i #i #i "i) S B =0 2 To see that this is a pure state (superposition, not mixture, of "i #i and #i "i) requires access to both and B For an observer who only sees, effective state is mixed: B = 1 2 ( "ih" + #ih# ) S =ln2 (Classically, if whole is in a definite state then each part is also: S apple S B )
5 Entanglement Entropy In general: if ρ is state of full system, then effective state for subsystem is =Tr c Entanglement entropy is defined as von Neumann entropy of subsystem: S = Tr ln Not necessarily due only to entanglement (for example, in thermal state, S includes thermal entropy) Obeys many important properties, such as: Subadditivity: S B apple S + S B Strong subadditivity: (Lieb-Ruskai 73) S B + S BC S B + S BC B C
6 Entanglement Entropy in QFT In quantum field theories (& many-body systems), spatial regions are highly entangled with each other Consider microwave cavity Even in ground state, electromagnetic field fluctuates: zero-point quantum fluctuations of modes Each mode is distributed in space => fluctuations are spatially correlated => any part of cavity is entangled with rest
7 Entanglement Entropy in QFT In quantum field theories (& many-body systems), spatial regions are highly entangled with each other S depends on: parameters of theory state size and shape of region S is ultraviolet divergent due to entanglement of short-wavelength modes Finite pieces contain physically meaningful information Examples: Critical (conformal) theory in : (Holzhey-Larsen-Wilczek 94; Calabrese-Cardy 03) d =2 Gapped theory in : d =1 length(@) central charge S = L S = c 3 ln L t finite temperature, also extensive term: s(t)volume() L correlation length S = area(@) d 1 + L short-distance cutoff topological entanglement entropy (Kitaev-Preskill 05; Levin-Wen 05)
8 Entanglement Entropy in QFT In quantum field theories (& many-body systems), spatial regions are highly entangled with each other S Entropy depends on: parameters of theory state size and shape of region Powerful new way to think about QFTs and many-body systems: quantum criticality topological order renormalization-group flows energy conditions many-body localization quenches much more In general, difficult to compute even in free theories Simplifies in certain theories with many strongly-interacting fields
9 N SU(n) Consider a QFT with for example N Holographic dualities interacting fields Yang-Mills theory, N n 2 When is large, these fields may admit a collective description in terms of a small number of degrees of freedom classical (think of hydrodynamics) usually complicated However, in certain cases, when the fields are very strongly interacting, it simplifies dramatically: General relativity in d + 1 dimensions with cosmological constant Λ < 0, coupled to a small number of matter fields, subject to certain boundary conditions universe in a box (Maldacena 97)
10 Holographic dualities If QFT is conformal (scale-invariant), ground state is anti-de Sitter (ds) spacetime: ds radius d dimensions of QFT ds 2 = R2 z 2 dt 2 + dz 2 + d~x 2 extra dimension z = boundary of ds, where field theory lives ~x z Map between boundary and bulk is non-local If QFT is gapped (confining), space ends on wall at z max (correlation length) Many specific examples known in various dimensions (mostly supersymmetric, derived from string theory)
11 Holographic Dualities QFT N thermodynamic limit N!1 statistical fluctuations collective modes deconfined plasma S / N ds radius GR R d 1 G N ~ classical limit ~! 0 quantum fluctuations gravitational waves, etc. black hole S = area(horizon) 4G N ~ Planck area Holographic dualities are useful for computing many things in strongly interacting QFTs Let s talk about entanglement entropies... horizon
12 Holographic Entanglement Entropy Ryu-Takayanagi 06: S = area(m ) 4G N ~ / N m = minimal surface anchored z ~x Democratizes Bekenstein-Hawking Entanglement = geometry
13 Holographic Entanglement Entropy Ryu-Takayanagi 06: S = area(m ) 4G N ~ Geometrizes entanglement: m = minimal surface anchored z ~x rea-law UV divergence due to infinite area of near boundary m d =1 Conformal theory in : S = c 3 ln L m Gapped theory: wall imposes IR cutoff on entanglement (Klebanov, Kutasov, Murugan 07) Finite temperature: minimal surface hugs horizon => extensive entropy s(t)volume() m m wall horizon
14 Holographic Entanglement Entropy Quantum information theory is built into spacetime geometry Example: Strong subadditivity S B + S BC S BC + S B B C B C B C S B + S BC = = = S BC + S B (MH-Takayanagi 07) In fact, RT formula obeys all general properties of entanglement entropies (Hayden-MH-Maloney 11; MH 13) lso has special properties, such as phase transitions (MH 10) B B m B m B S B = S + S B S B <S + S B
15 Holographic Entanglement Entropy Where are the bits? (MH-Freedman 16) Rewrite RT formula, using max flow-min cut theorem S = max # of bit threads leaving Each bit thread has cross section of 4 Planck areas Represents entangled pair of qubits between and complement, or mixed qubit of horizon Clarifies how bits are distributed among different regions (conditional entropies, mutual informations, etc.)
16 Holographic Entanglement Entropy Many other issues: Entanglement entropies in specific systems General properties Derivation Quantum (1/N) corrections Time dependence... The big one: Does space emerge from entanglement? From bit threads?
17 Holographic Entanglement Entropy Many other issues: Entanglement entropies in specific systems General properties Derivation Quantum (1/N) corrections Time dependence... The big one: Does space emerge from entanglement? From bit threads?
18
19
20 Classical and Quantum Gravity General relativity: Gravity is a manifestation of the curvature of spacetime Geometry of spacetime (metric g µ ) is dynamical Einstein equation: G µ =8 G N T µ g µ Classical theory. curvature matter cosmological constant We know of many quantum theories of gravity (from string theory,... ). t long distances (compared to Planck length), they reduce to GR. They have various numbers of dimensions types of matter fields values of Unfortunately, we don t understand them well enough to directly answer the above questions.
21 Holographic Dualities Suppose we have a quantum theory of gravity in d +1 dimensions ( d =2, 3,... ). = 1 R 2 R l P 1 Simplest solution to Einstein equation is anti-de Sitter (ds) spacetime. No matter ( T µ =0). Space is hyperbolic (Lobachevsky) space. Boundary is infinitely far away, with infinite potential wall. Light can reach boundary (and reflect back) in finite time. quantum gravity hyperbolic space Let spacetime geometry fluctuate, fixing boundary conditions at infinity. Closed quantum system.
22 Holographic Dualities Maldacena 97: Quantum gravity in d +1dimensions with ds boundary conditions = d dimensional ordinary quantum field theory (without gravity). QFT lives on the boundary. Map between the two theories is non-local. quantum gravity QFT has a large number of strongly interacting fields: N = R l P d 1 = Rd 1 G N ~ 1 QFT
23 This helps to understand black hole entropy. But mysteries remain. Nothing special happens at a black hole horizon. What about other surfaces? Can their areas represent entropies? re there entropies that are intrinsic to a system --- not thermal?
24 Holographic Entanglement Entropy Black hole = thermal state Maldacena 01: 2 black holes joined by Einstein-Rosen bridge = 2 entangled QFTs S = a 4G N ~ B Ryu, Takayanagi 06 proposed that, in general, S = a 4G N ~ area of minimal surface between and B B Entanglement is the fabric of spacetime Simple & beautiful... widely applied... but is it right?
25 Holographic Entanglement Entropy MH 10: Explained how to apply replica trick to holographic theories. Debunked previous derivation of holographic formula. Showed that holographic formula predicts phase transition for separated regions. Confirmed using Euclidean quantum gravity & orbifold CFT techniques. Lewkowycz, Maldacena 13: General derivation of holographic formula. B B S B = S + S B S B <S + S B
26 Time-Dependent Holographic Entanglement Entropy What about time? Original (Ryu-Takayanagi) holographic formula assumes state is static. Hubeny, Rangamani, Takayanagi 07: For non-static states, replace minimal surface in bulk space with extremal surface in bulk spacetime. Simple & beautiful... widely applied... but is it right? Callan, He, MH 12: Obeys strong subadditivity in examples. Extremal surface goes behind horizons! MH, Hubeny, Lawrence, Rangamani 14: Nonetheless obeys causality. Implies that QFT state is encoded by (part of) spacetime behind horizon. MH, Myers, Wien 14: Proved that area of a general surface (not just extremal) is given by differential entropy in QFT.
27 Entanglement entropy in holographic theories: Enormous progress in recent years. Still many mysteries. Suggests a deep and general connection between entanglement and the geometry of spacetime. (How) does spacetime itself emerge from quantum mechanics? Stay tuned... Summary
28 Entanglement entropy in holographic theories: Enormous progress in recent years. Still many mysteries. Suggests a deep and general connection between entanglement and the geometry of spacetime. (How) does spacetime itself emerge from quantum mechanics? Stay tuned... Summary
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 informationQuantum 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 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 informationProperties 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 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 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 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 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. (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 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 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 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 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 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 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 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 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 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 informationThe holographic approach to critical points. Johannes Oberreuter (University of Amsterdam)
The holographic approach to critical points Johannes Oberreuter (University of Amsterdam) Scale invariance power spectrum of CMB P s (k) / k n s 1 Lambda archive WMAP We need to understand critical points!
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 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 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 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 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 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 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 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 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 informationGeneralized entropy(ies) depending only on the probability; Gravitation, AdS/CFT,..
Generalized entropy(ies) depending only on the probability; Gravitation, AdS/CFT,.. December, 2014 Contenido 1 Generalized information entropies depending on the probability Contenido 1 Generalized information
More informationA 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 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 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 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 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 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 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 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 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 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 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 informationBLACK HOLE ENTROPY ENTANGLEMENT AND HOLOGRAPHIC SPACETIME. Ted Jacobson University of Maryland
BLACK HOLE ENTROPY ENTANGLEMENT AND HOLOGRAPHIC SPACETIME Ted Jacobson University of Maryland Goddard Scientific Colloquium, Feb. 7, 2018 Holographic principle Information paradox geometry from entanglement
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 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 informationBlack 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 informationWhy 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 informationAdS/CFT duality. Agnese Bissi. March 26, Fundamental Problems in Quantum Physics Erice. Mathematical Institute University of Oxford
AdS/CFT duality Agnese Bissi Mathematical Institute University of Oxford March 26, 2015 Fundamental Problems in Quantum Physics Erice What is it about? AdS=Anti de Sitter Maximally symmetric solution of
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 informationHolographic methods for cosmology. Gonzalo Torroba Stanford University
Holographic methods for cosmology Gonzalo Torroba Stanford University Observations and Theoretical Challenges in Primordial Cosmology KITP, UCSB, April 2013 Members of the collaboration Matt Dodelson Shunji
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 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 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 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 informationThe Quantum Spacetime
The Quantum Spacetime Juan Maldacena School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, USA. Abstract Rapporteur talk at the 2011 Solvay Conference 1 Opening It is a great pleasure
More informationA Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula
A Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula Arshad Momen and Tapobrata Sarkar the Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11 4014 Trieste, Italy
More informationSpacetime versus the Quantum
Spacetime versus the Quantum Joseph Polchinski UCSB Faculty Research Lecture, Dec. 12, 2014 God does not play dice with the world (Albert Einstein, 1926) vs. God does not play dice with the world (Albert
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 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 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 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 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 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 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 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 informationEmergent Spacetime. Udit Gupta. May 14, 2018
Emergent Spacetime Udit Gupta May 14, 2018 Abstract There have been recent theoretical hints that spacetime should not be thought of as a fundamental concept but rather as an emergent property of an underlying
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 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 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 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 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 informationBlack hole thermodynamics under the microscope
DELTA 2013 January 11, 2013 Outline Introduction Main Ideas 1 : Understanding black hole (BH) thermodynamics as arising from an averaging of degrees of freedom via the renormalisation group. Go beyond
More informationHolographic 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 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 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 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 informationGauge / 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 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 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 informationEntropic Force between Two Distant Black Holes in a Background Temperature
Entropic Force between Two Distant Black Holes in a Background Temperature Davoud Kamani Faculty of Physics, Amirkabir University of Technology (Tehran Polytechnic) Tehran, Iran Abstract: We use the Newton
More informationEMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE
EMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE Master Colloquium Pranjal Dhole University of Bonn Supervisors: Prof. Dr. Claus Kiefer Prof. Dr. Pavel Kroupa May 22, 2015 Work done at: Institute
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 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 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 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 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 informationIf I only had a Brane
If I only had a Brane A Story about Gravity and QCD. on 20 slides and in 40 minutes. AdS/CFT correspondence = Anti de Sitter / Conformal field theory correspondence. Chapter 1: String Theory in a nutshell.
More informationSymmetries, 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 informationBlack Holes, Quantum Mechanics, and Firewalls
Black Holes, Quantum Mechanics, and Firewalls Joseph Polchinski Simons Symposium, NYC 11/18/13 A Brief History of the Black Hole Information Paradox: A Brief History of the Black Hole Information Paradox:
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 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 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 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 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 informationAn equal area law for the van der Waals transition of holographic entanglement entropy
UTTG-18-15 TCC-007-15 An equal area law for the van der Waals transition of holographic entanglement entropy arxiv:1508.01955v2 [hep-th] 16 Aug 2015 Phuc H. Nguyen a,b a Theory Group, Department of Physics,
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 informationA Brief Introduction to AdS/CFT Correspondence
Department of Physics Universidad de los Andes Bogota, Colombia 2011 Outline of the Talk Outline of the Talk Introduction Outline of the Talk Introduction Motivation Outline of the Talk Introduction Motivation
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 informationTheory 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 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 information