AdS/CFT and strong subadditivity of entanglement entropy

Journal of High Energy Physics

Volumn 2007, Issue 2, 2007, Pages

  Hirata, Tomoyoshi ^a   Takayanagi, Tadashi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

AdS CFT correspondence; Black holes in string theory; Gauge gravity correspondence

Indexed keywords

EID: 33947677685     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/02/042     Document Type: Article

References (47)

1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity 1998 Adv. Theor. Math. Phys. 2 231 [1999 Int. J. Theor. Phys. 38 1113 ] [hep-th/9711200].
2. 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
3. M. Srednicki, Entropy and area 1993 Phys. Rev. Lett. 71 666 [hep-th/9303048].
4. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT 2006 Phys. Rev. Lett. 96 181602 [hep-th/0603001].
5. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy 2006 J. High Energy Phys. JHEP08(2006)045 [hep-th/0605073].
6. C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory 1994 Nucl. Phys. B 424 443 [hep-th/9403108]
7. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory J. Stat. Mech. (2004) P06002 [hep-th/0405152].
8. R. Emparan, Black hole entropy as entanglement entropy: a holographic derivation 2006 J. High Energy Phys. JHEP06(2006)012 [hep-th/0603081].
9. S.N. Solodukhin, Entanglement entropy of black holes and AdS/CFT correspondence 2006 Phys. Rev. Lett. 97 201601 [hep-th/0606205].
10. Y. Iwashita, T. Kobayashi, T. Shiromizu and H. Yoshino, Holographic entanglement entropy of de Sitter braneworld 2006 Phys. Rev. D 74 064027 [hep-th/0606027].
11. 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].
12. J.M. Maldacena, Eternal black holes in Anti-de-Sitter 2003 J. High Energy Phys. JHEP04(2003)021 [hep-th/0106112].
13. D.V. Fursaev, Proof of the holographic formula for entanglement entropy 2006 J. High Energy Phys. JHEP09(2006)018 [hep-th/0606184].
14. 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]
15. E. Witten, Anti-de Sitter space and holography 1998 Adv. Theor. Math. Phys. 2 253 [hep-th/9802150].
16. R. Bousso, A covariant entropy conjecture 1999 J. High Energy Phys. JHEP07(1999)004 [hep-th/9905177]
17. E. Witten, Holography in general space-times 1999 J. High Energy Phys. JHEP06(1999)028 [hep-th/9906022].
18. E.H. Lieb and M.B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy 1973 J. Math. Phys. 14 1938.
19. H. Casini and M. Huerta, A finite entanglement entropy and the C-theorem 2004 Phys. Lett. B 600 142 [hep-th/0405111].
20. H. Casini, Geometric entropy, area and strong subadditivity 2004 Class. Quantum Grav. 21 2351 [hep-th/0312238].
21. H. Casini and M. Huerta, Universal terms for the entanglement entropy in 2+1 dimensions 2007 Nucl. Phys. B 764 183 [hep-th/0606256].
22. D.V. Fursaev, Entanglement entropy in critical phenomena and analogue models of quantum gravity 2006 Phys. Rev. D 73 124025 [hep-th/0602134].
23. E. Fradkin and J. E. Moore, Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum [cond-mat/0605683].
24. J.M. Maldacena, Wilson loops in large-N field theories 1998 Phys. Rev. Lett. 80 4859 [hep-th/9803002]
25. 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].
26. H. Araki and E.H. Lieb, Entropy inequalities 1970 Comm. Math. Phys. 18 160.
27. See for example, M. Nielsen, and I.L. Chuang, Quantum computation and quantum information (Cambridge University Press) (2000).
28. J. Aczel, B. Forte and C.T. Ng, Why the Shannon and Hartley entropies are natural 1974 Adv. Appl. Prob. 6 131
29. W. Ochs, A new axiomatic characterization of the von Neumann entropy 1975 Rep. Math. Phys. 8 109
30. A. Wehrl, General properties of entropy 1978 Rev. Mod. Phys. 50 221.
31. S.N. Solodukhin, The conical singularity and quantum corrections to entropy of black hole 1995 Phys. Rev. D 51 609 [hep-th/9407001]
32. A. Wehrl, On 'nongeometric' contribution to the entropy of black hole due to quantum corrections 1995 Phys. Rev. D 51 618 [hep-th/9408068]
33. A. Wehrl, One loop renormalization of black hole entropy due to nonminimally coupled matter 1995 Phys. Rev. D 52 7046 [hep-th/9504022].
34. H. Casini, C.D. Fosco and M. Huerta, Entanglement and α entropies for a massive Dirac field in two dimensions J. Stat. Mech. (2005) P07007 [cond-mat/0505563]
35. H. Casini and M. Huerta, Entanglement and α entropies for a massive scalar field in two dimensions J. Stat. Mech. (2005) P12012 [cond-mat/0511014].
36. L. Susskind, The world as a hologram 1995 J. Math. Phys. 36 6377 [hep-th/9409089].
37. I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(n+m) gauge theories, 2000 Nucl. Phys. B 578 123 [hep-th/0002159]
38. 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].
39. N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces 1999 Phys. Rev. D 60 125006 [hep-th/9904191].
40. 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].
41. K. Zarembo, Wilson loop correlator in the AdS/CFT correspondence 1999 Phys. Lett. B 459 527 [hep-th/9904149].
42. P. Olesen and K. Zarembo, Phase transition in Wilson loop correlator from AdS/CFT correspondence [hep-th/0009210].
43. H. Kim, D.K. Park, S. Tamarian and H.J.W. Muller-Kirsten, Gross-Ooguri phase transition at zero and finite temperature: two circular wilson loop case 2001 J. High Energy Phys. JHEP03(2001)003 [hep-th/0101235].
44. 5: some periodic ansatze 2006 J. High Energy Phys. JHEP01(2006)056 [hep-th/0506058].
45. C. Bachas, Convexity of the quarkonium potential 1986 Phys. Rev. D 33 2723.
46. J. Greensite and P. Olesen, Worldsheet fluctuations and the heavy quark potential in the AdS/CFT approach 1999 J. High Energy Phys. JHEP04(1999)001 [hep-th/9901057].
47. H. Dorn and V.D. Pershin, Concavity of the q anti-q potential in N ≤ 4 super yang- mills gauge theory and AdS/CFT duality 1999 Phys. Lett. B 461 338 [hep-th/9906073]