## Equivalence of emergent de Sitter spaces from conformal field theory

## Abstract

Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a space-like slice of the asymptotically anti-de Sitter bulk is two-dimensional de Sitter space (dS _{2}), with a metric that can be derived from the entanglement entropy of intervals in the CFT. In the second proposal, de Sitter dynamics emerges naturally from the first law of entanglement entropy for perturbations around the vacuum state of CFTs. We provide support for the equivalence of these two emergent spacetimes in the vacuum case and beyond. In particular, we study the kinematic spaces of nontrivial solutions of 3d gravity, including the BTZ black string, BTZ black hole, and conical singularities. We argue that the resulting spaces are generically globally hyperbolic spacetimes that support dynamics given boundary conditions at future infinity. For the BTZ black string, corresponding to a thermal state of the CFT, we show that both prescriptions lead to an emergent hyperbolic patch of dS _{2}. As a result, we offer a general method for relating kinematic space and the auxiliary de Sitter space that is validmore »

- Authors:

- Columbia Univ., New York, NY (United States)
- Columbia Univ., New York, NY (United States); Instituut voor Theoretische Fysica, Leuven (Belgium)

- Publication Date:

- Research Org.:
- Columbia Univ., New York, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1360131

- Grant/Contract Number:
- SC0011941

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; AdS-CFT correspondence; conformal field theory; spacetime singularities

### Citation Formats

```
Asplund, Curtis T., Callebaut, Nele, and Zukowski, Claire. Equivalence of emergent de Sitter spaces from conformal field theory. United States: N. p., 2016.
Web. doi:10.1007/JHEP09(2016)154.
```

```
Asplund, Curtis T., Callebaut, Nele, & Zukowski, Claire. Equivalence of emergent de Sitter spaces from conformal field theory. United States. doi:10.1007/JHEP09(2016)154.
```

```
Asplund, Curtis T., Callebaut, Nele, and Zukowski, Claire. Tue .
"Equivalence of emergent de Sitter spaces from conformal field theory". United States. doi:10.1007/JHEP09(2016)154. https://www.osti.gov/servlets/purl/1360131.
```

```
@article{osti_1360131,
```

title = {Equivalence of emergent de Sitter spaces from conformal field theory},

author = {Asplund, Curtis T. and Callebaut, Nele and Zukowski, Claire},

abstractNote = {Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a space-like slice of the asymptotically anti-de Sitter bulk is two-dimensional de Sitter space (dS2), with a metric that can be derived from the entanglement entropy of intervals in the CFT. In the second proposal, de Sitter dynamics emerges naturally from the first law of entanglement entropy for perturbations around the vacuum state of CFTs. We provide support for the equivalence of these two emergent spacetimes in the vacuum case and beyond. In particular, we study the kinematic spaces of nontrivial solutions of 3d gravity, including the BTZ black string, BTZ black hole, and conical singularities. We argue that the resulting spaces are generically globally hyperbolic spacetimes that support dynamics given boundary conditions at future infinity. For the BTZ black string, corresponding to a thermal state of the CFT, we show that both prescriptions lead to an emergent hyperbolic patch of dS2. As a result, we offer a general method for relating kinematic space and the auxiliary de Sitter space that is valid in the vacuum and thermal cases.},

doi = {10.1007/JHEP09(2016)154},

journal = {Journal of High Energy Physics (Online)},

number = 9,

volume = 2016,

place = {United States},

year = {2016},

month = {9}

}

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