Holographic Rényi entropies at finite coupling

Journal of High Energy Physics

Volumn 2013, Issue 8, 2013, Pages

  Galante, Damián A ^a,b   Myers, Robert C ^a  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

AdS CFT Correspondence; Gauge gravity correspondence

Indexed keywords

EID: 84884549208     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP08(2013)063     Document Type: Article

References (73)

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 ] [ INSPIRE ].
3. A. Hamma, R. Ionicioiu and P. Zanardi, Ground state entanglement and geometric entropy in the Kitaev model, Phys. Lett. A 337 (2005) 22 [ quant-ph/0406202 ].
4. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [ hep-th/0405152 ] [ INSPIRE ].
5. 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 ] [ INSPIRE ]. (Pubitemid 44110594)
6. P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [ arXiv:0905.4013 ] [ INSPIRE ].
7. R.D. Sorkin, On the Entropy of the Vacuum Outside a Horizon, in General Relativity and Gravitation, volume 1, B. Bertotti, F. de Felice and A. Pascolini eds. (1983).
8. L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D 34 (1986) 373 [ INSPIRE ].
9. M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [ hep-th/9303048 ] [ INSPIRE ].
10. V.P. Frolov and I. Novikov, Dynamical origin of the entropy of a black hole, Phys. Rev. D 48 (1993) 4545 [ gr-qc/9309001 ] [ INSPIRE ].
11. L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [ hep-th/9401070 ] [ INSPIRE ].
12. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [ hep-th/0603001 ] [ INSPIRE ].
13. S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [ hep-th/0605073 ] [ INSPIRE ]. (Pubitemid 44330349)
14. T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: an Overview, J. Phys. A 42 (2009) 504008 [ arXiv:0905.0932 ] [ INSPIRE ].
15. T. Takayanagi, Entanglement Entropy from a Holographic Viewpoint, Class. Quant. Grav. 29 (2012) 153001 [ arXiv:1204.2450 ] [ INSPIRE ].
16. A. Rényi, On measures of information and entropy, in proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, volume 1, (1960) pg. 547, University of California Press, Berkeley, CA, U.S.A. (1961) [ http://digitalassets.lib.berkeley.edu/math/ucb/text/math-s4-v1-article-27.pdf ].
17. A. Rényi, On the foundations of information theory, Rev. Int. Stat. Inst. 33 (1965) 1.
18. K. Zyczkowski, Renyi extrapolation of Shannon entropy, Open Syst. Inf. Dyn. 10 (2003) 297 [ quant-ph/0305062 ]. (Pubitemid 39063823)
19. C. Beck and F. Schlögl, Thermodynamics of chaotic systems, Cambridge University Press, Cambridge, U.K. (1993).
20. P. Calabrese and A. Lefevre, Entanglement spectrum in one-dimensional systems, Phys. Rev. A 78 (2008) 032329 [ arXiv:0806.3059 ].
21. S.T. Flammia, A. Hamma, T.L. Hughes and X.-G. Wen, Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure, Phys. Rev. Lett. 103 (2009) 261601 [ arXiv:0909.3305 ].
22. M.A. Metlitski, C.A. Fuertes and S. Sachdev, Entanglement entropy in the O(N) model, Phys. Rev. B 80 (2009) 115122 [ arXiv:0904.4477 ].
23. M.B. Hastings, I. González, A.B. Kallin and R.G. Melko, Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations, Phys. Rev. Lett. 104 (2010) 157201 [ arXiv:1001.2335 ].
24. A. Lewkowycz, R.C. Myers and M. Smolkin, Observations on entanglement entropy in massive QFT's, JHEP 04 (2013) 017 [ arXiv:1210.6858 ] [ INSPIRE ].
25. C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [ hep-th/9401072 ] [ INSPIRE ].
26. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [ hep-th/9711200 ] [ INSPIRE ].
27. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [ hep-th/9905111 ] [ INSPIRE ].
28. M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [ INSPIRE ].
29. M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [ arXiv:1005.3035 ] [ INSPIRE ].
30. V.E. Hubeny and M. Rangamani, Causal Holographic Information, JHEP 06 (2012) 114 [ arXiv:1204.1698 ] [ INSPIRE ].
31. B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The Gravity Dual of a Density Matrix, Class. Quant. Grav. 29 (2012) 155009 [ arXiv:1204.1330 ] [ INSPIRE ].
32. E. Bianchi and R.C. Myers, On the Architecture of Spacetime Geometry, arXiv:1212.5183 [ INSPIRE ].
33. H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [ arXiv:1102.0440 ] [ INSPIRE ].
34. R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [ arXiv:1006.1263 ] [ INSPIRE ].
35. R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [ arXiv:1011.5819 ] [ INSPIRE ].
36. L.-Y. Hung, R.C. Myers and M. Smolkin, On Holographic Entanglement Entropy and Higher Curvature Gravity, JHEP 04 (2011) 025 [ arXiv:1101.5813 ] [ INSPIRE ].
37. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Entanglement Entropy in Lovelock Gravities, JHEP 07 (2011) 109 [ arXiv:1101.5781 ] [ INSPIRE ].
38. A. Bhattacharyya, A. Kaviraj and A. Sinha, Entanglement entropy in higher derivative holography, arXiv:1305.6694 [ INSPIRE ].
39. M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [ arXiv:1006.0047 ] [ INSPIRE ].
40. T. Faulkner, The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT, arXiv:1303.7221 [ INSPIRE ].
41. T. Hartman, Entanglement Entropy at Large Central Charge, arXiv:1303.6955 [ INSPIRE ].
42. A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, arXiv:1304.4926 [ INSPIRE ].
43. L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic Calculations of Renyi Entropy, JHEP 12 (2011) 047 [ arXiv:1110.1084 ] [ INSPIRE ].
44. R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [ gr-qc/9307038 ] [ INSPIRE ].
45. T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [ gr-qc/9312023 ] [ INSPIRE ].
46. 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 ] [ INSPIRE ].
47. I.R. Klebanov, S.S. Pufu, S. Sachdev and B.R. Safdi, Renyi Entropies for Free Field Theories, JHEP 04 (2012) 074 [ arXiv:1111.6290 ] [ INSPIRE ].
48. D.J. Gross and E. Witten, Superstring Modifications of Einstein's Equations, Nucl. Phys. B 277 (1986) 1 [ INSPIRE ].
49. M.T. Grisaru, A. 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 [ INSPIRE ].
50. M.T. Grisaru and D. Zanon, σ-model superstring corrections to the Einstein-Hilbert action, Phys. Lett. B 177 (1986) 347 [ INSPIRE ].
51. M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [ hep-th/9701093 ] [ INSPIRE ].
52. M.B. Green and C. Stahn, D3-branes on the Coulomb branch and instantons, JHEP 09 (2003) 052 [ hep-th/0308061 ] [ INSPIRE ].
53. M.F. Paulos, Higher derivative terms including the Ramond-Ramond five-form, JHEP 10 (2008) 047 [ arXiv:0804.0763 ] [ INSPIRE ].
54. R.C. Myers, M.F. Paulos and A. Sinha, Quantum corrections to eta/s, Phys. Rev. D 79 (2009) 041901 [ arXiv:0806.2156 ] [ INSPIRE ].
55. S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [ hep-th/9805156 ] [ INSPIRE ].
56. 3). JHEP 09 (1998) 010 [ hep-th/9808126 ] [ INSPIRE ].
57. A. Fotopoulos and T. Taylor, Comment on two loop free energy in N = 4 supersymmetric Yang-Mills theory at finite temperature, Phys. Rev. D 59 (1999) 061701 [ hep-th/9811224 ] [ INSPIRE ].
58. D. Fursaev, Entanglement Renyi Entropies in Conformal Field Theories and Holography, JHEP 05 (2012) 080 [ arXiv:1201.1702 ] [ INSPIRE ].
59. S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [ arXiv:0802.3117 ] [ INSPIRE ].
60. 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 ] [ INSPIRE ].
61. S. Gubser, I.R. Klebanov and A. Peet, Entropy and temperature of black 3-branes, Phys. Rev. D 54 (1996) 3915 [ hep-th/9602135 ] [ INSPIRE ].
62. B. Swingle, Structure of entanglement in regulated Lorentz invariant field theories, arXiv:1304.6402 [ INSPIRE ].
63. P.S. Howe and P.C. West, The Complete N = 2, D = 10 Supergravity, Nucl. Phys. B 238 (1984) 181 [ INSPIRE ].
64. J.H. Schwarz and P.C. West, Symmetries and Transformations of Chiral N = 2 D = 10 Supergravity, Phys. Lett. B 126 (1983) 301 [ INSPIRE ].
65. J.H. Schwarz, Covariant Field Equations of Chiral N = 2 D = 10 Supergravity, Nucl. Phys. B 226 (1983) 269 [ INSPIRE ].
66. 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 ] [ INSPIRE ].
67. A. Buchel, J.T. Liu and A.O. Starinets, Coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 707 (2005) 56 [ hep-th/0406264 ] [ INSPIRE ]. (Pubitemid 40131224)
68. M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [ hep-th/9806087 ] [ INSPIRE ].
69. V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [ hep-th/9902121 ] [ INSPIRE ].
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 ] [ INSPIRE ].
71. B. Swingle, Mutual information and the structure of entanglement in quantum field theory, arXiv:1010.4038 [ INSPIRE ].
72. H. Casini, Entropy inequalities from reflection positivity, J. Stat. Mech. 1008 (2010) P08019 [ arXiv:1004.4599 ] [ INSPIRE ].
73. L.Y. Hung, R.C. Myers and M. Smolkin, Twist operators in higher dimensions, in preparation.