Towards a derivation of holographic entanglement entropy

Journal of High Energy Physics

Volumn 2011, Issue 5, 2011, Pages

  Casini, Horacio ^a   Huerta, Marina ^a   Myers, Robert C ^b  

^a INSTITUTO BALSEIRO   (Argentina)

^b PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

AdS CFT correspondence; Holography and condensed matter physics (AdS CMT)

Indexed keywords

EID: 80053144636     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP05(2011)036     Document Type: Article

References (100)

1. M. Levin and X.G. Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96 (2006) 110405 [cond-mat/0510613].
2. A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 [hep-th/0510092].
3. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002 [hep-th/0405152].
4. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory: A non- technical introduction, Int. J. Quant. Inf. 4 (2006) 429 [quant-ph/0505193].
5. B. Hsu, M. Mulligan, E. Fradkin and E.-A. Kim, Universal entanglement entropy in 2D conformal quantum critical points, arXiv:0812.0203.
6. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001].
7. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073].
8. I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140].
9. M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939.
10. M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [arXiv:1005.3035].
11. M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047].
12. D.V. Fursaev, Proof of the holographic formula for entanglement entropy, JHEP 09 (2006) 018 [hep-th/0606184].
13. T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: An overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932].
14. L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP 04 (2011) 025 [arXiv:1101.5813].
15. C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072].
16. R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263].
17. R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819].
18. H. Casini and M. Huerta, Entanglement entropy for the n-sphere, Phys. Lett. B 694 (2010) 167 [arXiv:1007.1813].
19. P. Candelas and J.S. Dowker, Field theories on conformally related space-times: Some global considerations, Phys. Rev. D 19 (1979) 2902.
20. S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117].
21. M.J. Duff, Observations on conformal anomalies, Nucl. Phys. B 125 (1977) 334.
22. M.J. Duff, Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994) 1387 [hep-th/9308075]. (Pubitemid 24791825)
23. S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047].
24. J.S. Dowker, Entanglement entropy for even spheres, arXiv:1009.3854.
25. J.S. Dowker, Hyperspherical entanglement entropy, J. Phys. A 43 (2010) 445402 [arXiv:1007.3865].
26. S.N. Solodukhin, Entanglement entropy of round spheres, Phys. Lett. B 693 (2010) 605 [arXiv:1008.4314].
27. J.S. Dowker, Entanglement entropy for odd spheres, arXiv:1012.1548.
28. R. Haag, Local quantum physics: Fields, particles, algebras, Springer, U.S.A. (1992).
29. H. Li and F.D.M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum Hall effect states, Phys. Rev. Lett. 101 (2008) 010504 [arXiv:0805.0332].
30. P. Calabrese and A. Lefevre, Entanglement spectrum in one-dimensional systems, Phys. Rev. A 78 (2008) 032329.
31. A.M. Turner, F. Pollmann and E. Berg, Topological phases of one-dimensional fermions: An entanglement point of view, Phys. Rev. B 83 (2011) 075102 [arXiv:1008.4346].
32. L. Fidkowski, Entanglement spectrum of topological insulators and superconductors, Phys. Rev. Lett. 104 (2010) 130502 [arXiv:0909.2654].
33. H. Yao and X.-L. Qi, Entanglement entropy and entanglement spectrum of the Kitaev model, Phys. Rev. Lett. 105 (2010) 080501 [arXiv:1001.1165].
34. J.J. Bisognano and E.H. Wichmann, On the duality condition for quantum fields, J. Math. Phys. 17 (1976) 303.
35. J.J. Bisognano and E.H. Wichmann, On the duality condition for a hermitian scalar field, J. Math. Phys. 16 (1975) 985.
36. W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870.
37. P.D. Hislop and R. Longo, Modular structure of the local algebras associated with the free massless scalar field theory, Commun. Math. Phys. 84 (1982) 71.
38. H. Casini and M. Huerta, Remarks on the entanglement entropy for disconnected regions, JHEP 03 (2009) 048 [arXiv:0812.1773].
39. R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero-energy states, JHEP 06 (1999) 036 [hep-th/9906040].
40. S. Aminneborg, I. Bengtsson, S. Holst and P. Peldan, Making Anti-de Sitter black holes, Class. Quant. Grav. 13 (1996) 2707 [gr-qc/9604005].
41. D.R. Brill, J. Louko and P. Peldan, Thermodynamics of (3 + 1)-dimensional black holes with toroidal or higher genus horizons, Phys. Rev. D 56 (1997) 3600 [gr-qc/9705012].
42. L. Vanzo, Black holes with unusual topology, Phys. Rev. D 56 (1997) 6475 [gr-qc/9705004].
43. R.B. Mann, Pair production of topological Anti-de Sitter black holes, Class. Quant. Grav. 14 (1997) L109 [gr-qc/9607071].
44. D. Birmingham, Topological black holes in Anti-de Sitter space, Class. Quant. Grav. 16 (1999) 1197 [hep-th/9808032].
45. R. Emparan, AdS membranes wrapped on surfaces of arbitrary genus, Phys. Lett. B 432 (1998) 74 [hep-th/9804031].
46. D.J. Gross and J.H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B 291 (1987) 41.
47. C.G. Callan Jr., E.J. Martinec, M.J. Perry and D. Friedan, Strings in background fields, Nucl. Phys. B 262 (1985) 593.
48. R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055].
49. A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257].
50. J. de Boer, M. Kulaxizi and A. Parnachev, AdS7/CFT6, Gauss-Bonnet gravity and viscosity bound, JHEP 03 (2010) 087 [arXiv:0910.5347].
51. X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160].
52. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Lovelock gravities and black holes, JHEP 06 (2010) 008 [arXiv:0912.1877].
53. X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944].
54. X.O. Camanho, J.D. Edelstein and M.F. Paulos, Lovelock theories, holography and the fate of the viscosity bound, arXiv:1010.1682.
55. D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498.
56. D. Lovelock, Divergence-free tensorial concomitants, Aequat. Math. 4 (1970) 127.
57. R.C. Myers and B. Robinson, Black holes in quasi-topological gravity, JHEP 08 (2010) 067 [arXiv:1003.5357].
58. R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038].
59. T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023].
60. V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028].
61. N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982), p. 340.
62. R. Laamme, Geometry and thermofields, Nucl. Phys. B 324 (1989) 233.
63. D.V. Fursaev and G. Miele, Finite temperature scalar field theory in static de Sitter space, Phys. Rev. D 49 (1994) 987 [hep-th/9302078].
64. D.V. Vassilevich, Heat kernel expansion: User's manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138].
65. L.S. Brown and J.P. Cassidy, Stress tensors and their trace anomalies in conformally at space-times, Phys. Rev. D 16 (1977) 1712.
66. T.S. Bunch and P.C.W. Davies, Quantum field theory in de Sitter space: Renormalization by point splitting, Proc. Roy. Soc. Lond. A 360 (1978) 117.
67. L.Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic calculations of Renyi entropy in higher dimensions, in preparation.
68. M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087].
69. M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032].
70. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic entanglement entropy in Lovelock gravities, arXiv:1101.5781.
71. J.T. Liu, W. Sabra and Z. Zhao, Holographic c-theorems and higher derivative gravity, arXiv:1012.3382.
72. A. Sinha, On higher derivative gravity, c-theorems and cosmology, Class. Quant. Grav. 28 (2011) 085002 [arXiv:1008.4315].
73. M.F. Paulos, Holographic phase space: C-functions and black holes as renormalization group ows, arXiv:1101.5993.
74. L. Susskind and E. Witten, The holographic bound in Anti-de Sitter space, hep-th/9805114.
75. C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108].
76. A. Schwimmer and S. Theisen, Entanglement entropy, trace anomalies and holography, Nucl. Phys. B 801 (2008) 1 [arXiv:0802.1017].
77. H. Casini, Mutual information challenges entropy bounds, Class. Quant. Grav. 24 (2007) 1293 [gr-qc/0609126].
78. H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562].
79. B. Swingle, Mutual information and the structure of entanglement in quantum field theory, arXiv:1010.4038.
80. D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, arXiv:1012.3210.
81. D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, arXiv:1103.1181.
82. K.A. Intriligator and B. Wecht, The exact superconformal R-symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128].
83. E. Barnes, K.A. Intriligator, B. Wecht and J. Wright, Evidence for the strongest version of the 4D a-theorem, via a-maximization along RG ows, Nucl. Phys. B 702 (2004) 131 [hep-th/0408156].
84. D.J. Gross and E. Witten, Superstring modifications of Einstein's equations, Nucl. Phys. B 277 (1986) 1.
85. M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Four loop β-function for the N = 1 and N = 2 supersymmetric nonlinear σ-model in two-dimensions, Phys. Lett. B 173 (1986) 423.
86. M.F. Paulos, Higher derivative terms including the Ramond-Ramond five-form, JHEP 10 (2008) 047 [arXiv:0804.0763].
87. A. Buchel, R.C. Myers, M.F. Paulos and A. Sinha, Universal holographic hydrodynamics at finite coupling, Phys. Lett. B 669 (2008) 364 [arXiv:0808.1837].
88. M.B. Green and M. Gutperle, Effects of D-instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093].
89. R.C. Myers, M.F. Paulos and A. Sinha, Quantum corrections to η/s, Phys. Rev. D 79 (2009) 041901 [arXiv:0806.2156].
90. D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Universality of the operator product expansions of SCFT(4), Phys. Lett. B 394 (1997) 329 [hep-th/9608125].
91. D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042].
92. R. Lohmayer, H. Neuberger, A. Schwimmer and S. Theisen, Numerical determination of entanglement entropy for a sphere, Phys. Lett. B 685 (2010) 222 [arXiv:0911.4283].
93. A. Buchel, R.C. Myers and A. Sinha, Beyond η/s = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521].
94. Y. Kats and P. Petrov, Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044 [arXiv:0712.0743].
95. C.P. Bachas, P. Bain and M.B. Green, Curvature terms in D-brane actions and their M-theory origin, JHEP 05 (1999) 011 [hep-th/9903210].
96. J.M. Maldacena, Eternal black holes in Anti-de-Sitter, JHEP 04 (2003) 021 [hep-th/0106112].
97. D. Klemm, V. Moretti and L. Vanzo, Rotating topological black holes, Phys. Rev. D 57 (1998) 6127 [Erratum ibid. D 60 (1999) 109902] [gr-qc/9710123].
98. M.H. Dehghani, Rotating topological black holes in various dimensions and AdS/CFT correspondence, Phys. Rev. D 65 (2002) 124002 [hep-th/0203049].
99. R.B. Mann, Charged topological black hole pair creation, Nucl. Phys. B 516 (1998) 357 [hep-th/9705223].
100. R.-G. Cai and A. Wang, Thermodynamics and stability of hyperbolic charged black holes, Phys. Rev. D 70 (2004) 064013 [hep-th/0406057].