Abstract
We show that the anti-de Sitter(AdS) space naturally emerges from the conformal field theory (CFT). The behavior of the leading divergent term in the entanglement entropy implies the underlying AdS geometry. The coefficient of the leading divergent term is related to the radius of the AdS space. All these are confirmed fully for two-dimensional CFTs. We also give comments for higher dimensional CFTs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G.’ t Hooft, Salamfest 1993:0284–296 [gr-qc/9310026].
L. Susskind, J. Math. Phys. 36, 6377 (1995).
J. M. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999)
J. M. Maldacena, [Adv. Theor. Math. Phys. 2, 231 (1998)].
S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006).
S. Ryu and T. Takayanagi, J. High Energy Phys. 0608, 045 (2006)
H. Casini, M. Huerta and R. C. Myers, J. High Energy Phys. 1105, 036 (2011).
A. Lewkowycz and J. Maldacena, J. High Energy Phys. 1308, 090 (2013).
M. Van Raamsdonk, ar**v:0907.2939 [hep-th]
M. Van Raamsdonk, Gen. Rel. Grav. 42, 2323 (2010)
M. Van Raamsdonk, [Int. J. Mod. Phys. D 19, 2429 (2010)].
B. Swingle, Phys. Rev. D 86, 065007 (2012).
M. Nozaki, S. Ryu and T. Takayanagi, J. High Energy Phys. 1210, 193 (2012).
G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).
J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, Phys. Rev. Lett. 110, 100402 (2013).
C. Beny, New J. Phys. 15, 023020 (2013).
M. Miyaji and T. Takayanagi, PTEP 2015, 073B03 (2015).
F. Pastawski, B. Yoshida, D. Harlow and J. Preskill, J. High Energy Phys. 1506, 149 (2015).
B. Czech, L. Lamprou, S. McCandlish and J. Sully, J. High Energy Phys. 1510, 175 (2015).
M. Miyaji et al., Phys. Rev. Lett. 115, 171602 (2015).
P. Hayden et al., J. High Energy Phys. 1611, 009 (2016).
P. Caputa et al., Phys. Rev. Lett. 119, 071602 (2017).
S. S. Lee, Nucl. Phys. B 832, 567 (2010).
S. S. Lee, Nucl. Phys. B 851, 143 (2011).
S. S. Lee, J. High Energy Phys. 1210, 160 (2012).
C. Holzhey, F. Larsen and F. Wilczek, Nucl. Phys. B 424, 443 (1994).
P. Calabrese and J. L. Cardy, J. Stat. Mech. 0406, P06002 (2004).
J. D. Brown and M. Henneaux, Commun. Math. Phys. 104, 207 (1986).
L. Bombelli, R. K. Koul, J. Lee and R. D. Sorkin, Phys. Rev. D 34, 373 (1986).
M. Srednicki, Phys. Rev. Lett. 71, 666 (1993).
Acknowledgments
We would like to thank Jae-Suk Park and Kyung Kiu Kim for useful discussion. SH would like to thank KEK and KIAS for their hospitality, where part of this work has been done. This work was supported by the National Research Foundation of Korea (NRF) grant NRF-2016R1D1A1A09917598 and by the Yonsei University Future-leading Research Initiative of 2017 (2017-22-0098).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Hyun, S., Park, SA. AdS Space from Entanglement Entropy. J. Korean Phys. Soc. 75, 845–850 (2019). https://doi.org/10.3938/jkps.75.845
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.75.845