On holographic entanglement entropy and higher curvature gravity

Journal of High Energy Physics

Volumn 2011, Issue 4, 2011, Pages

  Hung, Ling Yan ^a   Myers, Robert C ^a   Smolkin, Michael ^a  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

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

Indexed keywords

EID: 80053122636     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP04(2011)025     Document Type: Article

References (89)

1. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001].
2. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073].
3. T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932].
4. M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047].
5. D.V. Fursaev, Proof of the holographic formula for entanglement entropy, JHEP 09 (2006) 018 [hep-th/0606184].
6. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002 [hep-th/0405152].
7. 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].
8. C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108].
9. M. Headrick and T. Takayanagi, A Holographic Proof of the Strong Subadditivity of Entanglement Entropy, Phys. Rev. D, 76 (2007) 106013 [arXiv:0704.3719].
10. J.M. Maldacena, Eternal black holes in Anti-de-Sitter, JHEP 04 (2003) 021 [hep-th/0106112].
11. C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072].
12. H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, arXiv:1102.0440.
13. R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038].
14. 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].
15. T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023].
16. D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498.
17. D. Lovelock, Divergence-free tensorial concomitants, Aequationes Math. 4 (1970) 127.
18. T. Jacobson and R.C. Myers, Black hole entropy and higher curvature interactions, Phys. Rev. Lett. 70 (1993) 3684 [hep-th/9305016].
19. S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117].
20. M. Kulaxizi, Higher Derivative Gravity and Entanglement Entropy, talk presented at Crete Conference On Gauge Theories And The Structure Of Spacetime, Kolymvari Crete, 11-18 September 2010, http://hep.physics.uoc.gr/conf09/.
21. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Entanglement Entropy in Lovelock Gravities, arXiv:1101.5781.
22. J.-R. Sun, Note on Chern-Simons Term Correction to Holographic Entanglement Entropy, JHEP 05 (2009) 061 [arXiv:0810.0967].
23. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Lovelock Gravities and Black Holes, JHEP 06 (2010) 008 [arXiv:0912.1877].
24. R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819].
25. Q. Exirifard and M.M. Sheikh-Jabbari, Lovelock Gravity at the Crossroads of Palatini and Metric Formulations, Phys. Lett. B 661 (2008) 158 [arXiv:0705.1879].
26. J.T. Wheeler, Symmetric Solutions to the Gauss-Bonnet Extended Einstein Equations, Nucl. Phys. B 268 (1986) 737.
27. J.T. Wheeler, Symmetric Solutions To The Maximally Gauss-Bonnet Extended Einstein Equations, Nucl. Phys. B 273 (1986) 732.
28. R.C. Myers and J.Z. Simon, Black Hole Thermodynamics in Lovelock Gravity, Phys. Rev. D 38 (1988) 2434.
29. R.C. Myers and J.Z. Simon, Black Hole Evaporation and Higher Derivative Gravity, Gen. Rel. Grav. 21 (1989) 761.
30. T.S. Bunch, Surface terms in higher derivative gravity, J. Phys. A 14 (1981) L139.
31. R.C. Myers, Higher Derivative Gravity, Surface Terms and String Theory, Phys. Rev. D 36 (1987) 392.
32. X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944].
33. X.O. Camanho, J.D. Edelstein and M.F. Paulos, Lovelock theories, holography and the fate of the viscosity bound, arXiv:1010.1682.
34. R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133].
35. S. Nojiri and S.D. Odintsov, Anti-de Sitter black hole thermodynamics in higher derivative gravity and new con ning-decon ning phases in dual CFT, Phys. Lett. B 521 (2001) 87 [Erratum ibid. B 542 (2002) 301] [hep-th/0109122].
36. Y.M. Cho and I.P. Neupane, Anti-de Sitter black holes, thermal phase transition and holography in higher curvature gravity, Phys. Rev. D 66 (2002) 024044 [hep-th/0202140].
37. I.P. Neupane, Black hole entropy in string-generated gravity models, Phys. Rev. D 67 (2003) 061501 [hep-th/0212092].
38. I.P. Neupane, Thermodynamic and gravitational instability on hyperbolic spaces, Phys. Rev. D 69 (2004) 084011 [hep-th/0302132].
39. R.-G. Cai, A note on thermodynamics of black holes in Lovelock gravity, Phys. Lett. B 582 (2004) 237 [hep-th/0311240].
40. M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805].
41. M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The Viscosity Bound and Causality Violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318].
42. A. Buchel and R.C. Myers, Causality of Holographic Hydrodynamics, JHEP 08 (2009) 016 [arXiv:0906.2922].
43. D.M. Hofman, Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625].
44. X.-H. Ge and S.-J. Sin, Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant, JHEP 05 (2009) 051 [arXiv:0903.2527].
45. R.-G. Cai, Z.-Y. Nie and Y.-W. Sun, Shear Viscosity from Effective Couplings of Gravitons, Phys. Rev. D 78 (2008) 126007 [arXiv:0811.1665].
46. R.-G. Cai, Z.-Y. Nie, N. Ohta and Y.-W. Sun, Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling, Phys. Rev. D 79 (2009) 066004 [arXiv:0901.1421].
47. 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].
48. A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257].
49. J. de Boer, M. Kulaxizi and A. Parnachev, AdS7=CFT6, Gauss-Bonnet Gravity and Viscosity Bound, JHEP 03 (2010) 087 [arXiv:0910.5347].
50. J.T. Liu, W. Sabra and Z. Zhao, Holographic c-theorems and higher derivative gravity, arXiv:1012.3382.
51. D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656.
52. R.C. Myers and B. Robinson, Black Holes in Quasi-topological Gravity, JHEP 08 (2010) 067 [arXiv:1003.5357].
53. M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087].
54. M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032].
55. S. Nojiri and S.D. Odintsov, On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence, Int. J. Mod. Phys. A 15 (2000) 413 [hep-th/9903033].
56. M. Blau, K.S. Narain and E. Gava, On subleading contributions to the AdS/CFT trace anomaly, JHEP 09 (1999) 018 [hep-th/9904179].
57. R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055].
58. C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Dieomorphisms and holographic anomalies, Class. Quant. Grav. 17 (2000) 1129 [hep-th/9910267].
59. A. Schwimmer and S. Theisen, Entanglement Entropy, Trace Anomalies and Holography, Nucl. Phys. B 801 (2008) 1 [arXiv:0802.1017].
60. R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263].
61. I. Racz and R.M. Wald, Extension of space-times with Killing horizon, Class. Quant. Grav. 9 (1992) 2643.
62. C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco U.S.A. (1973).
63. M.J. Du, Observations on Conformal Anomalies, Nucl. Phys. B 125 (1977) 334.
64. M.J. Du, Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994) 1387 [hep-th/9308075].
65. S. Deser and A. Schwimmer, Geometric classi cation of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047].
66. C. Feerman and C.R. Graham, Conformal Invariants, in Elie Cartan et les Math ematiques d'aujourdhui, Ast e risque (1985) pg. 95.
67. C. Feerman and C.R. Graham, The Ambient Metric, arXiv:0710.0919.
68. F. Bastianelli, S. Frolov and A.A. Tseytlin, Conformal anomaly of (2; 0) tensor multiplet in six dimensions and AdS/CFT correspondence, JHEP 02 (2000) 013 [hep-th/0001041].
69. M.F. Paulos, Holographic phase space: c-functions and black holes as renormalization group ows, arXiv:1101.5993.
70. R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238].
71. C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021].
72. A. Buchel, R.C. Myers and A. Sinha, Beyond =s = 1=4 , JHEP 03 (2009) 084 [arXiv:0812.2521].
73. 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].
74. A. Buchel, M.P. Heller and R.C. Myers, sQGP as hCFT, Phys. Lett. B 680 (2009) 521 [arXiv:0908.2802].
75. D.J. Gross and E. Witten, Superstring Modifications of Einstein's Equations, Nucl. Phys. B 277 (1986) 1.
76. M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Four Loop -function for the N = 1 and N = 2 Supersymmetric Nonlinear -model in Two-Dimensions, Phys. Lett. B 173 (1986) 423.
77. A. Buchel, R.C. Myers, M.F. Paulos and A. Sinha, Universal holographic hydrodynamics at nite coupling, Phys. Lett. B 669 (2008) 364 [arXiv:0808.1837].
78. R.C. Myers, M.F. Paulos and A. Sinha, Quantum corrections to =s, Phys. Rev. D 79 (2009) 041901 [arXiv:0806.2156].
79. 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].
80. 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].
81. Q.J. Ejaz, T. Faulkner, H. Liu, K. Rajagopal and U.A. Wiedemann, A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT, JHEP 04 (2008) 089 [arXiv:0712.0590].
82. 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].
83. V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant Holographic Entanglement Entropy Proposal, JHEP, 07 (2007) 062 [arXiv:0705.0016].
84. S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230].
85. M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG ow, JHEP 08 (2001) 041 [hep-th/0105276].
86. M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic Renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119].
87. K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067].
88. L.-Y. Hung, R.C. Myers and M. Smolkin, Some Calculable Contributions to Holographic Entanglement Entropy, in preparation.
89. M.H. Dehghani and Z. Dayyani, Lorentzian wormholes in Lovelock gravity, Phys. Rev. D 79 (2009) 064010 [arXiv:0903.4262].