de Sitter holography with a finite number of states

Maulik Parikh, Erik Verlinde

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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 languageEnglish (US)
Pages (from-to)1237-1257
Number of pages21
JournalJournal of High Energy Physics
Issue number1
DOIs
StatePublished - Jan 2005

Keywords

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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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