Entanglement entropy, trace anomalies and holography. (English) Zbl 1189.83036
Summary: The holographic representation of the entanglement entropy of four-dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the holographic representation are calculated by a method which does not require the solution of the equations of motion or a cut-off. The two calculations disagree for rather generic geometries. The reasons for the disagreement are analyzed.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 94A17 | Measures of information, entropy |
| 81T50 | Anomalies in quantum field theory |
References:
| [1] | Holzhey, C.; Larsen, F.; Wilczek, F., Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B, 424, 443 (1994) · Zbl 0990.81564 |
| [2] | Calabrese, P.; Cardy, J. L., Entanglement entropy and quantum field theory: A non-technical introduction, Int. J. Quantum Inf., 4, 429 (2006) · Zbl 1097.81014 |
| [3] | Ryu, S.; Takayanagi, T., Aspects of holographic entanglement entropy, JHEP, 0608, 045 (2006) |
| [4] | Fursaev, D. V., Proof of the holographic formula for entanglement entropy, JHEP, 0609, 018 (2006) |
| [5] | Klebanov, I. R.; Kutasov, D.; Murugan, A., Entanglement as a probe of confinement · Zbl 1219.81214 |
| [6] | Nishioka, T.; Takayanagi, T., AdS bubbles, entropy and closed string tachyons, JHEP, 0701, 090 (2007) |
| [7] | Henningson, M.; Skenderis, K., Weyl anomaly for Wilson surfaces, JHEP, 9906, 012 (1999) · Zbl 0961.81106 |
| [8] | Gustavsson, A., On the Weyl anomaly of Wilson surfaces, JHEP, 0312, 059 (2003) |
| [9] | Asnin, V., Analyticity properties of Graham-Witten anomalies · Zbl 1180.81123 |
| [10] | Imbimbo, C.; Schwimmer, A.; Theisen, S.; Yankielowicz, S., Diffeomorphisms and holographic anomalies, Class. Quantum Grav., 17, 1129 (2000) · Zbl 0952.81052 |
| [11] | Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 |
| [12] | C. Fefferman, R. Graham, Conformal Invariants, Astèrisque, Hors Série, 1995, p. 95; C. Fefferman, R. Graham, Conformal Invariants, Astèrisque, Hors Série, 1995, p. 95 |
| [13] | Henningson, M.; Skenderis, K., The holographic Weyl anomaly, JHEP, 9807, 023 (1998) · Zbl 0958.81083 |
| [14] | Rendall, A. D., Asymptotics of solutions of the Einstein equations with positive cosmological constant, Ann. Henri Poincare, 5, 1041 (2004) · Zbl 1061.83008 |
| [15] | Schwimmer, A.; Theisen, S., Universal features of holographic anomalies, JHEP, 0310, 001 (2003) |
| [16] | Papadimitriou, I.; Skenderis, K., Thermodynamics of asymptotically locally AdS spacetimes, JHEP, 0508, 004 (2005) |
| [17] | Graham, C. R.; Witten, E., Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B, 546, 52 (1999) · Zbl 0944.81046 |
| [18] | Fursaev, D. V.; Solodukhin, S. N., On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D, 54, 2133 (1995) |
| [19] | Wess, J.; Zumino, B., Consequences of anomalous Ward identities, Phys. Lett. B, 37, 95 (1971) |
| [20] | Fradkin, E. S.; Tseytlin, A. A., Conformal anomaly in Weyl theory and anomaly free superconformal theories, Phys. Lett. B, 134, 187 (1984) · Zbl 0967.83513 |
| [21] | Bianchi, M.; Freedman, D. Z.; Skenderis, K., Holographic renormalization, Nucl. Phys. B, 631, 159 (2002) · Zbl 0995.81075 |
| [22] | Boulanger, N., Algebraic classification of Weyl anomalies in arbitrary dimensions, Phys. Rev. Lett., 98, 261302 (2007) · Zbl 1228.81252 |
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