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Entanglement entropy and gravity/condensed matter correspondence

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Abstract

The entanglement entropy has been very important in various subjects such as the quantum information theory, condensed matter physics and quantum gravity. Especially, for more than twenty years, this quantity has been studied by many people in order to obtain a quantum mechanical interpretation of the gravitational entropy such as the black hole entropy. We will introduce recent progresses toward this long-standing problem in quantum gravity by applying the idea of holography, especially the AdS/CFT correspondence found in string theory. We will explain the holographic formula which computes the entanglement entropy of quantum field theories in terms of the area of minimal surfaces in general relativity. We will also review the recent application of AdS/CFT correspondence to condensed matter physics from the viewpoint of entanglement entropy.

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Acknowledgments

TT would like to thank all of his collaborators on this subject, especially Mathew Headrick, Veronika Hubeny, Tatsuma Nishioka, Mukund Rangamani and Shinsei Ryu. TT is very grateful to organizers of the GR20/Amaldi10 conference for the wonderful hospitality. TT is supported by JSPS Grant-in-Aid for Scientific Research (B) No. 25287058 and JSPS Grant-in-Aid for Challenging Exploratory Research No. 24654057. TT is also supported by World Premier International Research Center Initiative (WPI Initiative) from the Japan Ministry of Education, Culture, Sports, Science and Technology (MEXT).

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  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto,  606-8502, Japan

    Tadashi Takayanagi

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Correspondence to Tadashi Takayanagi.

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This article belongs to the Topical Collection: The First Century of General Relativity: GR20/Amaldi10.

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Takayanagi, T. Entanglement entropy and gravity/condensed matter correspondence. Gen Relativ Gravit 46, 1693 (2014). https://doi.org/10.1007/s10714-014-1693-3

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