### Abstract

We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hubert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representations, we show that it is possible to construct an S-matrix that is finite-dimensional, unitary, and de Sitter-invariant. We present a class of examples that realize this idea holographically in terms of spinor fields on the boundary sphere. The finite dimensionality is due to Fermi statistics and an "exclusion principle" that truncates the orthonormal basis in which the spinor fields can be expanded.

Original language | English (US) |
---|---|

Pages (from-to) | 1237-1257 |

Number of pages | 21 |

Journal | Journal of High Energy Physics |

Issue number | 1 |

State | Published - Jan 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- AdS-CFT and dS-CFT Correspondence
- Space-Time Symmetries

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*, (1), 1237-1257.

**de Sitter holography with a finite number of states.** / Parikh, Maulik; Verlinde, Erik.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, no. 1, pp. 1237-1257.

}

TY - JOUR

T1 - de Sitter holography with a finite number of states

AU - Parikh, Maulik

AU - Verlinde, Erik

PY - 2005/1

Y1 - 2005/1

N2 - We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hubert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representations, we show that it is possible to construct an S-matrix that is finite-dimensional, unitary, and de Sitter-invariant. We present a class of examples that realize this idea holographically in terms of spinor fields on the boundary sphere. The finite dimensionality is due to Fermi statistics and an "exclusion principle" that truncates the orthonormal basis in which the spinor fields can be expanded.

AB - We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hubert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representations, we show that it is possible to construct an S-matrix that is finite-dimensional, unitary, and de Sitter-invariant. We present a class of examples that realize this idea holographically in terms of spinor fields on the boundary sphere. The finite dimensionality is due to Fermi statistics and an "exclusion principle" that truncates the orthonormal basis in which the spinor fields can be expanded.

KW - AdS-CFT and dS-CFT Correspondence

KW - Space-Time Symmetries

UR - http://www.scopus.com/inward/record.url?scp=27344443430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27344443430&partnerID=8YFLogxK

M3 - Article

SP - 1237

EP - 1257

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1029-8479

IS - 1

ER -