TY - JOUR

T1 - Holographic entanglement entropy

T2 - An overview

AU - Nishioka, Tatsuma

AU - Ryu, Shinsei

AU - Takayanagi, Tadashi

N1 - Funding Information:
We thank M. Kloster for detailed comments and discussions. We also acknowledge helpful discussions with D. Kessler, Q. Ouyang, L. Tang, and J. Widom. This research is supported by the NSF through Grants No. DMR-0211308 and No. MCB-0083704.

PY - 2009

Y1 - 2009

N2 - In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the AdS/CFT relates physical observables in strongly coupled quantum many-body systems to certain classical quantities in gravity plus matter theories. In the case of our holographic entanglement entropy, its gravity dual turns out to be purely geometric, i.e. the area of minimal area surfaces in AdS spaces. One interesting application is to study various phase transitions by regarding the entanglement entropy as order parameters. Indeed we will see that our holographic calculations nicely reproduce the confinement/deconfinement transition. Our results can also be applied to understanding the microscopic origins of black hole entropy.

AB - In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the AdS/CFT relates physical observables in strongly coupled quantum many-body systems to certain classical quantities in gravity plus matter theories. In the case of our holographic entanglement entropy, its gravity dual turns out to be purely geometric, i.e. the area of minimal area surfaces in AdS spaces. One interesting application is to study various phase transitions by regarding the entanglement entropy as order parameters. Indeed we will see that our holographic calculations nicely reproduce the confinement/deconfinement transition. Our results can also be applied to understanding the microscopic origins of black hole entropy.

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U2 - 10.1088/1751-8113/42/50/504008

DO - 10.1088/1751-8113/42/50/504008

M3 - Article

AN - SCOPUS:75849163829

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 50

M1 - 504008

ER -