Aspects of holographic entanglement entropy

Journal of High Energy Physics

Volumn 2006, Issue 8, 2006, Pages

  Ryu, Shinsei ^a   Takayanagi, Tadashi ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

AdS CFT Correspondence; Black Holes in String Theory; Brane Dynamics in Gauge Theories; Gauge gravity correspondence

Indexed keywords

EID: 33748289532     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/08/045     Document Type: Article

References (96)

1. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT 2006 Phys. Rev. Lett. 96 181602 [hep-th/0603001]
2. C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory 1994 Nucl. Phys. B 424 443 [hep-th/9403108]
3. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory J. Stat. Mech. 0406 (2004) P002 [hep-th/0405152]
4. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory: a non- technical introduction 2006 Int. J. Quant. Inf. 4 429 [quant-ph/0505193]
5. G. Vidal, J.I. Latorre, E. Rico and A. Kitaev, Entanglement in quantum critical phenomena 2003 Phys. Rev. Lett. 90 227902 [quant-ph/0211074]
6. J.I. Latorre, E. Rico and G. Vidal, Ground state entanglement in quantum spin chains [quant-ph/0304098]
7. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity 1998 Adv. Theor. Math. Phys. 2 231 [hep-th/9711200]
8. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity 2000 Phys. Rep. 323 183 [hep-th/9905111]
9. S. Hawking, J.M. Maldacena and A. Strominger, Desitter entropy, quantum entanglement and AdS/CFT 2001 J. High Energy Phys. JHEP05(2001)001 [hep-th/0002145]
10. J.M. Maldacena, Eternal black holes in anti-de-Sitter 2003 J. High Energy Phys. JHEP04(2003)021 [hep-th/0106112]
11. G. 't Hooft, Dimensional reduction in quantum gravity [gr-qc/9310026]
12. L. Susskind, The world as a hologram 1995 J. Math. Phys. 36 6377 [hep-th/9409089]
13. D. Bigatti and L. Susskind, TASI lectures on the holographic principle [hep-th/0002044]
14. R. Bousso, A covariant entropy conjecture 1999 J. High Energy Phys. JHEP07(1999)004 [hep-th/9905177]
15. R. Bousso, Holography in general space-times 1999 J. High Energy Phys. JHEP06(1999)028 [hep-th/9906022]
16. R. Emparan, Black hole entropy as entanglement entropy: a holographic derivation 2006 J. High Energy Phys. JHEP06(2006)012 [hep-th/0603081]
17. R. Brustein, M.B. Einhorn and A. Yarom, Entanglement interpretation of black hole entropy in string theory 2006 J. High Energy Phys. JHEP01(2006)098 [hep-th/0508217]
18. M.J. Duff, String triality, black hole entropy and Cayley's hyperdeterminant [hep-th/0601134]
19. R. Kallosh and A. Linde, Strings, black holes and quantum information 2006 Phys. Rev. D 73 104033 [hep-th/0602061]
20. P. Levay, Stringy black holes and the geometry of entanglement 2006 Phys. Rev. D 74 024030 [hep-th/0603136]
21. L. Bombelli, R.K. Koul, J.-H. Lee and R.D. Sorkin, A quantum source of entropy for black holes 1986 Phys. Rev. D 34 373
22. M. Srednicki, Entropy and area 1993 Phys. Rev. Lett. 71 666 [hep-th/9303048]
23. See for example, Quantum field theory of many-body systems (Oxford University Press), 2004
24. F. Alet, A. M. Walczak, M. P. A. Fisher, Exotic quantum phases and phase transitions in correlated matter [cond-mat/0511516]
25. G. Misguich and C. Lhuillier, Two-dimensional quantum antiferromagnets in Frustrated spin systems, H.T. Diep ed., World-Scientific, 2005, [cond-mat/0310405]
26. I. Peschel, On the entanglement entropy for a XY spin chain J. Stat. Mech. (2004) P12005 [cond-mat/0410416]
27. B.Q. Jin, and V.E. Korepin, Quantum spin chain, Toeplitz determinants and Fisher-Hartwig conjecture J. Stat. Phys. 116 (2004) 79 [quant-ph/0304108]
28. A.R. Its, B.Q. Jin, V.E. Korepin, Entanglement in XY spin chain J. Phys. A: Math. Gen. 38 (2005) 2975 [quant-ph/0409027]
29. A. Kitaev and J. Preskill, Topological entanglement entropy 2006 Phys. Rev. Lett. 96 110404 [hep-th/0510092]
30. M. Levin and X.G. Wen, Detecting topological order in a ground state wave function Phys. Rev. Lett. 96 (2006) 110405 [cond-mat/0510613]
31. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory 1998 Phys. Lett. B 428 105 [hep-th/9802109]
32. E. Witten, Anti-de Sitter space and holography 1998 Adv. Theor. Math. Phys. 2 253 [hep-th/9802150]
33. See for example, M. Nielsen, and I.L. Chuang, Quantum computation and quantum information Cambridge university press, 2000
34. M.B. Plenio, J. Eisert, J. Dreissig and M. Cramer, Entropy, entanglement and area: analytical results for harmonic lattice systems 2005 Phys. Rev. Lett. 94 060503 [quant-ph/0405142]
35. M.B. Plenio, J. Eisert, J. Dreissig and M. Cramer, An entanglement-area law for general bosonic harmonic lattice systems 2006 Phys. Rev. A 73 012309 [quant-ph/0505092]
36. S. Das and S. Shankaranarayanan, How robust is the entanglement entropy - area relation? 2006 Phys. Rev. D 73 121701 [gr-qc/0511066]
37. H. Casini, Geometric entropy, area and strong subadditivity 2004 Class. Quantum Grav. 21 2351 [hep-th/0312238]
38. M.M. Wolf, Violation of the entropic area law for fermions 2006 Phys. Rev. Lett. 96 010404 [quant-ph/0503219]
39. D. Gioev, and I. Klich, Entanglement entropy of fermions in any dimension and the Widom conjecture 2006 Phys. Rev. Lett. 96 100503 [quant-ph/0504151]
40. T. Barthel, M.C. Chung, U. Schollwock, Entanglement scaling in critical two-dimensional fermionic and bosonic systems [cond-mat/0602077]
41. W. Li, L. Ding, R. Yu, T. Roscilde, S. Hass, Scaling behavior of entanglement in two- and three-dimensional free fermions [quant-ph/0602094]
42. G. 't Hooft, On the quantum structure of a black hole 1985 Nucl. Phys. B 256 727
43. L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory 1994 Phys. Rev. D 50 2700 [hep-th/9401070]
44. T.M. Fiola, J. Preskill, A. Strominger and S.P. Trivedi, Black hole thermodynamics and information loss in two- dimensions 1994 Phys. Rev. D 50 3987 [hep-th/9403137]
45. H. Casini, C.D. Fosco and M. Huerta, Entanglement and alpha entropies for a massive Dirac field in two dimensions J. Stat. Mech. (2005) P07007 [cond-mat/0505563]
46. V.G. Knizhnik, Analytic fields on riemannian surfaces 1986 Phys. Lett. B 180 247
47. V.G. Knizhnik, Analytic fields on riemann surfaces. 2 1987 Comm. Math. Phys. 112 567
48. H. Casini and M. Huerta, Entanglement and alpha entropies for a massive scalar field in two dimensions 2005 J. Stat. Mech. (2005) P12012 [cond-mat/0511014]
49. D. Kabat, Black hole entropy and entropy of entanglement 1995 Nucl. Phys. B 453 281 [hep-th/9503016]
50. D.V. Fursaev, Entanglement entropy in critical phenomena and analogue models of quantum gravity 2006 Phys. Rev. D 73 124025 [hep-th/0602134]
51. H. Casini and M. Huerta, A finite entanglement entropy and the C-theorem 2004 Phys. Lett. B 600 142 [hep-th/0405111]
52. A.B. Zamolodchikov, 'Irreversibility' of the flux of the renormalization group in a 2D field theory 1986 Sov. Phys. JETP Lett. 43 730
53. J.I. Latorre, C.A. Lutken, E. Rico and G. Vidal, Fine-grained entanglement loss along renormalization group flows 2005 Phys. Rev. A 71 034301 [quant-ph/0404120]
54. H.Q. Zhou, T. Barthel, J.O. Fjaerestad, U. Schollwoeck, Entanglement and boundary critical phenomena [cond-mat/0511732]
55. R. Orus, Entanglement and majorization in (1+1)-dimensional quantum systems 2005 2006 Phys. Rev. A 71 052327 [Erratum-ibid. A 73 019904] [quant-ph/0501110]
56. S.N. Solodukhin, Entropy of schwarzschild black hole and string-black hole correspondence 1998 Phys. Rev. D 57 2410 [hep-th/9701106]
57. J.L. Cardy, Is there a C theorem in four-dimensions? 1988 Phys. Lett. B 215 749
58. H. Osborn and G.M. Shore, Correlation functions of the energy momentum tensor on spaces of constant curvature 2000 Nucl. Phys. B 571 287 [hep-th/9909043]
59. D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories 1998 Nucl. Phys. B 526 543 [hep-th/9708042]
60. D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories 1998 Phys. Rev. D 57 7570 [hep-th/9711035]
61. S.S. Gubser, Einstein manifolds and conformal field theories 1999 Phys. Rev. D 59 025006 [hep-th/9807164]
62. D.V. Fursaev and S.N. Solodukhin, On the description of the riemannian geometry in the presence of conical defects 1995 Phys. Rev. D 52 2133 [hep-th/9501127]
63. S.N. Solodukhin, The conical singularity and quantum corrections to entropy of black hole 1995 Phys. Rev. D 51 609 [hep-th/9407001]
64. S.N. Solodukhin, On 'nongeometric' contribution to the entropy of black hole due to quantum corrections 1995 Phys. Rev. D 51 618 [hep-th/9408068]
65. S.N. Solodukhin, One loop renormalization of black hole entropy due to nonminimally coupled matter 1995 Phys. Rev. D 52 7046 [hep-th/9504022]
66. S.S. Gubser, I.R. Klebanov and A.W. Peet, Entropy and temperature of black 3-branes 1996 Phys. Rev. D 54 3915 [hep-th/9602135]
67. S.D. Mathur, The fuzzball proposal for black holes: an elementary review 2005 Fortschr. Phys. 53 793 [hep-th/0502050]
68. C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence 1999 Nucl. Phys. B 546 52 [hep-th/9901021]
69. V. Balasubramanian and S.F. Ross, Holographic particle detection 2000 Phys. Rev. D 61 044007 [hep-th/9906226]
70. J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity 1986 Comm. Math. Phys. 104 207
71. L. Susskind and E. Witten, The holographic bound in anti-de Sitter space [hep-th/9805114]
72. T. Okuda and T. Takayanagi, Ghost D-branes 2006 J. High Energy Phys. JHEP03(2006)062 [hep-th/0601024]
73. M. Bãados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time 1992 Phys. Rev. Lett. 69 1849 [hep-th/9204099]
74. 3 black holes and a stringy exclusion principle 1998 J. High Energy Phys. JHEP12(1998)005 [hep-th/9804085]
75. I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities 2000 J. High Energy Phys. JHEP08(2000)052 [hep-th/0007191]
76. J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory [hep-th/0003136]
77. J.M. Maldacena and C. Ñez, Towards the large-N limit of pure N ≤ 1 super Yang-Mills 2001 Phys. Rev. Lett. 86 588 [hep-th/0008001]
78. J.M. Maldacena, Wilson loops in large-N field theories 1998 Phys. Rev. Lett. 80 4859 [hep-th/9803002]
79. S.J. Rey and J.T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity 2001 Eur. Phys. J. C 22 379 [hep-th/9803001]
80. D. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large-N limit 1999 Phys. Rev. D 59 105023 [hep-th/9809188]
81. D.J. Gross and H. Ooguri, Aspects of large-N gauge theory dynamics as seen by string theory 1998 Phys. Rev. D 58 106002 [hep-th/9805129]
82. M. Henningson and K. Skenderis, The holographic Weyl anomaly 1998 J. High Energy Phys. JHEP07(1998)023 [hep-th/9806087]
83. V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity 1999 Comm. Math. Phys. 208 413 [hep-th/9902121]
84. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories 1998 Adv. Theor. Math. Phys. 2 505 [hep-th/9803131]
85. S.J. Rey, S. Theisen and J.T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity 1998 Nucl. Phys. B 527 171 [hep-th/9803135]
86. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature 1998 Phys. Lett. B 434 36 [hep-th/9803137]
87. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops, confinement and phase transitions in large-N gauge theories from supergravity 1998 J. High Energy Phys. JHEP06(1998)001 [hep-th/9803263]
88. O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The hagedorn/deconfinement phase transition in weakly coupled large-N gauge theories 2004 Adv. Theor. Math. Phys. 8 603 [hep-th/0310285]
89. S. Ryu, and Y. Hatsugai, Entanglement entropy and Berry phases in solid states [cond-mat/0601237]
90. N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges 1998 Phys. Rev. D 58 046004 [hep-th/9802042]
91. C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons 1991 Nucl. Phys. B 359 611
92. O. Aharony, A brief review of 'little string theories' 2000 Class. Quantum Grav. 17 929 [hep-th/9911147]
93. E. Witten, Quantum gravity in de Sitter space [hep-th/0106109]
94. A. Strominger, The dS/CFT correspondence 2001 J. High Energy Phys. JHEP10(2001)034 [hep-th/0106113]
95. E.K. Boyda, S. Ganguli, P. Horava and U. Varadarajan, Holographic protection of chronology in universes of the Gödel type 2003 Phys. Rev. D 67 106003 [hep-th/0212087]
96. T. Harmark and T. Takayanagi, Supersymmetric Gödel universes in string theory 2003 Nucl. Phys. B 662 3 [hep-th/0301206]