# Entanglement Entropy of Black Holes and Anti-de Sitter Space/Conformal-Field-Theory Correspondence

## Abstract

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L{sup 2}lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.

- Authors:

- School of Engineering and Science, International University Bremen, P.O. Box 750561, Bremen 28759 (Germany)

- Publication Date:

- OSTI Identifier:
- 20861138

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 97; Journal Issue: 20; Other Information: DOI: 10.1103/PhysRevLett.97.201601; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; CONFORMAL INVARIANCE; DE SITTER GROUP; ENTROPY; QUANTUM ENTANGLEMENT; QUANTUM FIELD THEORY; QUANTUM MECHANICS; SUPERGRAVITY

### Citation Formats

```
Solodukhin, Sergey N.
```*Entanglement Entropy of Black Holes and Anti-de Sitter Space/Conformal-Field-Theory Correspondence*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVLETT.97.201601.

```
Solodukhin, Sergey N.
```*Entanglement Entropy of Black Holes and Anti-de Sitter Space/Conformal-Field-Theory Correspondence*. United States. doi:10.1103/PHYSREVLETT.97.201601.

```
Solodukhin, Sergey N. Fri .
"Entanglement Entropy of Black Holes and Anti-de Sitter Space/Conformal-Field-Theory Correspondence". United States.
doi:10.1103/PHYSREVLETT.97.201601.
```

```
@article{osti_20861138,
```

title = {Entanglement Entropy of Black Holes and Anti-de Sitter Space/Conformal-Field-Theory Correspondence},

author = {Solodukhin, Sergey N.},

abstractNote = {A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L{sup 2}lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.},

doi = {10.1103/PHYSREVLETT.97.201601},

journal = {Physical Review Letters},

number = 20,

volume = 97,

place = {United States},

year = {Fri Nov 17 00:00:00 EST 2006},

month = {Fri Nov 17 00:00:00 EST 2006}

}